Dissertations / Theses: 'Conjugate boundary value problems'

1

Degla, Guy Aymard. "A Maximum Principle for Conjugate BVPs." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/4320.

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2

Hopkins, Britney Henderson Johnny. "Multiplicity of positive solutions of even-order nonhomogeneous boundary value problems." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5323.

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3

Mohammed, Alip. "Boundary value problems of complex variables." [S.l. : s.n.], 2002. http://www.diss.fu-berlin.de/2003/23/index.html.

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4

Rabinovich, Vladimir, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "Boundary value problems in cuspidal wedges." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2536/.

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The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.

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5

Xiaochun, Liu, and Bert-Wolfgang Schulze. "Boundary value problems in edge representation." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2674/.

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Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.

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6

Schulze, Bert-Wolfgang, and Nikolai Tarkhanov. "Boundary value problems with Toeplitz conditions." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2983/.

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We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.

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7

Ashton, Anthony Charles Lewis. "Nonlocal approaches to boundary value problems." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/252204.

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8

Delecki, Zdzislaw Andrzej. "Boundary value problems in dielectric spectroscopy." Thesis, University of Ottawa (Canada), 1989. http://hdl.handle.net/10393/21430.

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9

Alsaedy, Ammar, and Nikolai Tarkhanov. "Normally solvable nonlinear boundary value problems." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6507/.

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We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.

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10

Traytak, Sergey D. "Boundary-value problems for the diffusion equation in domains with disconnected boundary: Boundary-value problems for the diffusion equation in domainswith disconnected boundary." Diffusion fundamentals 2 (2005) 38, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14368.

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11

Roman, Svetlana. "Green's functions for boundary-value problems with nonlocal boundary conditions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111227_092148-01085.

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In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introduction the topicality of the problem is defined, the goals and tasks of the research are formulated, the scientific novelty of the dissertation, the methodology of research, the practical value and the significance of the results are presented. m-order differential problem and its Green's function are investigated in the first chapter. The relation between two Green's functions and the existence condition of Green's function are obtained. In the second chapter, the main definitions and results of the first chapter are formulated for the second-order differential equation with additional conditions. In the examples the application of the received results is analyzed for problems with nonlocal boundary conditions in detail. In the third chapter, the second-order difference equation with two additional conditions is considered. The expression of Green's function and its existence... [to full text]
Disertacijoje tiriami antros ir aukštesnės eilės diferencialinis ir diskretusis uždaviniai su įvairiomis, tame tarpe ir nelokaliosiomis, sąlygomis, kurios yra aprašytos tiesiškai nepriklausomais tiesiniais funkcionalais. Pateikiamos šių uždavinių Gryno funkcijų išraiškos ir jų egzistavimo sąlygos, jei žinoma homogeninės lygties fundamentalioji sistema. Gautas dviejų Gryno funkcijų sąryšis uždaviniams su ta pačia lygtimi, bet su papildomomis sąlygomis. Rezultatai pritaikomi uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Įvadiniame skyriuje aprašyta tiriamoji problema ir temos objektas, išanalizuotas temos aktualumas, išdėstyti darbo tikslai, uždaviniai, naudojama tyrimų metodika, mokslinis darbo naujumas ir gautų rezultatų reikšmė, pateikti ginamieji teiginiai ir darbo rezultatų aprobavimas. m-tosios eilės diferencialinis uždavinys ir jo Gryno funkcija nagrinėjami pirmajame skyriuje. Surastas uždavinio sprendinys, išreikštas per Gryno funkciją. Pateikta Gryno funkcijos egzistavimo sąlyga. Antrajame skyriuje pateikti pirmojo skyriaus pagrindiniai apibrėžimai ir rezultatai antros eilės diferencialinei lygčiai. Pavyzdžiuose išsamiai išanalizuotas gautų rezultatų pritaikymas uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Trečiajame skyriuje nagrinėjama antros eilės diskrečioji lygtis su dviem sąlygomis. Surastos diskrečiosios Gryno funkcijos išraiška ir jos egzistavimo sąlyga. Taip pat pateiktas dviejų Gryno funkcijų sąryšis, kuris leidžia surasti diskrečiosios... [toliau žr. visą tekstą]

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12

Mugnolo, Delio. "Second order abstract initial-boundary value problems." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971647674.

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13

Schrohe, Elmar, and Bert-Wolfgang Schulze. "Edge-degenerate boundary value problems on cones." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2543/.

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We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.

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14

Rabinovich, Vladimir, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "Boundary value problems in domains with corners." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2555/.

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15

Harutyunyan, G., and Bert-Wolfgang Schulze. "Boundary value problems in weighted edge spaces." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3010/.

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We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.

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16

Schulze, Bert-Wolfgang. "Boundary value problems with the transmission property." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/3037/.

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We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.

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17

Kunkel, Curtis J. Henderson Johnny. "Positive solutions of singular boundary value problems." Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5022.

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18

Heredia, N. Fernando. "A new method for boundary value problems." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21467.

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19

Dyer, Luke Oliver. "Parabolic boundary value problems with rough coefficients." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33276.

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This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a relationship between the regularity and Dirichlet boundary value problems for parabolic equations of the form Lu = div(A∇u)−ut = 0 in Lip(1, 1/2) time-varying cylinders, where the coefficient matrix A = [aij(X, t)] is uniformly elliptic and bounded. We show that if the Regularity problem (R)p for the equation Lu = 0 is solvable for some 1 < p < then the Dirichlet problem (D*) 1 p, for the adjoint equation L*v = 0 is also solvable, where p' = p/(p − 1). This result is analogous to the one established in the elliptic case. In the second result we prove the solvability of the parabolic Lp Dirichlet boundary value problem for 1 < p ≤ ∞ for a PDE of the form ut = div(A∇u)+B ·∇u on time-varying domains where the coefficients A = [aij(X, t)] and B = [bi(X, t)] satisfy a small Carleson condition. This result brings the state of affairs in the parabolic setting up to the current elliptic standard. Furthermore, we establish that if the coefficients of the operator A and B satisfy a vanishing Carleson condition, and the time-varying domain is of VMO-type then the parabolic Lp Dirichlet boundary value problem is solvable for all 1 < p ≤ ∞. This is related to elliptic results where the normal of the boundary of the domain is in VMO or near VMO implies the invertibility of certain boundary operators in Lp for all 1 < p < ∞. This then (using the method of layer potentials) implies solvability of the Lp boundary value problem in the same range for certain elliptic PDE. We do not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover Lp solvability in the full range of p's as the elliptic case. Moreover, to achieve this result we give new equivalent and localisable definitions of the appropriate time-varying domains.

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20

Spence, Euan Alastair. "Boundary value problems for linear elliptic PDEs." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609476.

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21

Zhao, Kun. "Initial-boundary value problems in fluid dynamics modeling." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31778.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.
Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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22

Rutka, Vita. "Immersed interface methods for elliptic boundary value problems." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=974190918.

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23

Schulze, Bert-Wolfgang, Boris Sternin, and Victor Shatalov. "On general boundary value problems for elliptic equations." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2513/.

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We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.

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24

Schulze, Bert-Wolfgang, and Jörg Seiler. "The edge algebra structure of boundary value problems." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2595/.

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Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.

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25

Schulze, Bert-Wolfgang, and Jörg Seiler. "Pseudodifferential boundary value problems with global projection conditions." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2623/.

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Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero

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26

Windisch, G. "Exact discretizations of two-point boundary value problems." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800804.

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In the paper we construct exact three-point discretizations of linear and nonlinear two-point boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal M-matrices in the linear case and M-functions in the nonlinear case.

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27

Garcia, Maxine Patricia. "Collocation methods for mixed order boundary value problems." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322404.

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28

Matar, Samir A. "Numerical methods for high-order boundary-value problems." Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293058.

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29

Siddiqi, Shahid S. "Spline solutions of high-order boundary-value problems." Thesis, Brunel University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384827.

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30

Kassianidis, Fotios. "Boundary-value problems for transversely isotropic hyperelastic solids." Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/20/.

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In this thesis we examine three boundary-value problems combined with the presence of dead-load tractions in respect of transersely isotropic elastic materials. In particular, Chapter 1 mainly consists of existing preliminary remarks on the continuum (phenomenological) approach used here to study the mechanical response of elastic materials under large strains. More specifically, we discuss, always within the continuous framework, basic kinematical concepts, fundamental stress principles as well as balance laws; those also being appropriately specialized for material bodies under the state of equilibrium, i.e. for static problems. Description of the governing constitutive theory for Cauchy elastic isotropic and transversely isotropic solids follows, with reference to which, the notion of a hyperelastic solid is then prescribed. Further, the necessary connections with the classical linear theory of transversely isotropic solids are generated and finally some typical constitutive inequalities are summaraized. Then, in Chapter 2, we examine the classical problem of finite bending of a rectangular block of elastic material into a sector of a circular cylindrical tube in respect of compressible transversely isotropic elastic materials. More specifically, we consider the possible existence of isochoric solutions. In contrast to the corresponding problem for isotropic materials, for which such solutions do not exist for a compressible material [38], we determine conditions on the form of the strain-energy function for which isochoric solutions are possible. Based on those conditions, some general forms of strain-energy functions that admit isochoric bending are derived. We also, for the considered geometry and deformation, examine aspects of stability predicated on the notion of strong ellipticity. Expressly, for plane strain, we provide necessary and sufficient conditions for strong ellipticity to hold. The material incorporated in the chapter has been accepted for publication in [42]. In Chapter 3 we study the problem of (plane strain) azimuthal shear of a circular cylindrical tube of incompressible transversely isotropic elastic material subject to finite deformation. The preferred direction associated with the transverse isotropy lies in the planes normal to the tube axis and is disposed so as to preserve the cylindrical symmetry. For a general form of strain-energy function the considered deformation yields simple expressions for the azimuthal shear stress and the associated strong ellipticity condition in terms of the azimuthal shear strain. These apply for a sense of shear that is either 'with' or 'against' the preferred direction (anti-clockwise and clockwise, respectively), so that material line elements locally in the preferred direction either extend or (at least initially) contract, respectively. For some specific strain-energy functions we then examine local loss of uniqueness of the shear-strain relationship and failure of ellipticity for the case of contraction and the dependence on the geometry of the preferred direction. In particular, for a widely used reinforced neo-Hookean material (see e.g., [77, 63, 62, 47, 48]), we obtain closed-form solutions that determine the domain of strong ellipticity in terms of the relationship between the shear strain and the angle (in general, a function of the radius) between the tangent to the preferred direction and the undeformed radial direction. It is shown, in particular, that as the magnitude of the applied shear stress increases then, after loss of ellipticity, there are two admissible values for the shear strain at certain radial locations. Absoulutely stable deformations involve the lower magnitude value outside a certain radius and the higher magnitude value within this radius. The radius that separates the two values increases with with increasing magnitude of the shear stress. The results are illustrated graphically for two specific forms of energy function. The work of this chapter has been accepted for publication and will appear in [41]. Also, parts of this work have already been presented in SES-Penn State (2006) by the third author. In Chapter 4 we are concerned with circular cylindrical tubes composed of incompressible transversely isotropic elastic material subject to simultaneous finite axial extension, inflation and torsion. Here, a great deal of attention is given to the actual kinematics of the problem. Due to the incompressibility constraint, three independent deformaions quantities associated with each one of the processes comprising the combined deformation are identified. These serve, in essence, to measure stretch in the axial and azimuthal direction of the body as well as the amount of shear in the planes normal to its radial direction and hence they suffice to fully characterize the resulting strain. Analogously to the azimuthal shear problem examined in the previous chapter, the preferred direction associated with the transverse isotropy is distributed in the planes normal to the tube axis and is disposed so as, in any case, to preserve the cylindrical symmetry. For the considered geometry, the material line elements in the preferred direction always contract when axial extension of the tube is applied. Assuming that the body is held fixed in that extended state, inflation of the tube may be responsible for either further contraction (at least in early stages of the process) or relaxation of the preferred direction. In this situation, the sense of shear is of no importance since the torsional aspect of the deformation has no actual impact on the length of line aliments in that direction. The cylindrical polar components of the Cauchy stress tensor are written down by means of a general form of strain-energy function and then a new universal relation applying for the considered geometry and deformation is generated. In the special situation where the preferred direction lies along, in the undeformed configuration, the radial direction of the body, coaxiality between the Cauchy stress and the left stretch tensors is accomplished and the latter constitutive relation, under appropriate specialization, recovers a well known result holding in the corresponding isotropic theory (see, e.g., [32]). Finally, based on the governing equilibrium equations and in conjunction with the kinematics of the problem, we provide general formulas for the applied loads necessary to support the combined deformation. These are found to apply for a wide range of transversely isotropic materials as well as for isotropic materials. Analogous remarks are briefly made with respect to a specific class of cylindrically orthotropic tubes.

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31

Shepherd, Duncan Paul. "Theoretical fracture mechanics and elliptic boundary value problems." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243658.

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32

Kaye, Adelina E. "Singular integration with applications to boundary value problems." Kansas State University, 2016. http://hdl.handle.net/2097/32717.

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Master of Science
Mathematics
Nathan Albin
Pietro Poggi-Corradini
This report explores singular integration, both real and complex, focusing on the the Cauchy type integral, culminating in the proof of generalized Sokhotski-Plemelj formulae and the applications of such to a Riemann-Hilbert problem.

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33

Carrasco, Hugo Alexandre Sacristão. "Higher order boundary value problems on unbounded intervals." Doctoral thesis, Universidade de Évora, 2017. http://hdl.handle.net/10174/21093.

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The relative scarcity of results that guarantee the existence of solutions for BVP on unbounded domains, contrasts with the high applicability on real problems of differential equations defined on the half-line or on the whole real line. It is this gap the main reason that led to this work. The differential equations studied vary from second order to higher orders and they can be discontinuous on time. Different types of boundary conditions will be discussed herein, for example, Sturm- Liouville, homoclinic, Lidstone and functional conditions. The non-compactness of the time interval and the possibility of study unbounded functions will require the redefinition of the admissible Banach spaces. In fact the space considered and the functional framework assumed define the set of admissible solutions for each problem under a main goal: the functions must remain bounded for the space and the norm in consideration. This is achieved by defining some weight functions (polynomial or exponential) in the space or assuming some asymptotic behavior. In addition to the existence, solutions will be localized in a strip. The lower and upper solutions method will play an important role, and combined with other tools like the one-sided Nagumo growth conditions, Green’s functions or Schauder’s fixed point theorem, provide the existence and location results for differential equations with various boundary conditions. Different applications to real phenomena will be presented, most of them translated into classical equations as Duffing, Bernoulli-Eulerv. Karman, Fisher-Kolmogorov, Swift-Hohenberg, Emden-Fowler or Falkner-Skan-type equations. All these applications have a common denominator: they are defined in unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete problems; RESUMO: Problemas de valor na fronteira de ordem superior em intervalos não limitados A relativa escassez de resultados que garantam a existência de soluções para problemas de valor na fronteira, em domínios ilimitados, contrasta com a alta aplicabilidade em problemas reais de equações diferenciais definidas na semi reta ou em toda a reta real. É esta lacuna o principal motivo que conduziu a este trabalho. As equações diferenciais estudadas variam da segunda ordem a ordens superiores e podem ser descontínuas no tempo. As condições de fronteira aqui analisadas são de diferentes tipos, nomeadamente, Sturm - Liouville, homoclínicas, Lidstone e condições funcionais. A não compacidade do intervalo de tempo e a possibilidade de estudar funções ilimitadas, exigirá a redefinição dos espaços de Banach admissíveis. Na verdade, o espaço considerado e o quadro funcional assumido define o conjunto de soluções admissíveis para cada problema sob um objetivo principal: as funções devem permanecer limitadas para o espaço e norma considerados. Isto é conseguido através da definição de algumas "funções de peso" (polinomiais ou exponenciais) no espaço considerado ou assumindo um comportamento assintótico. Além da existência, as soluções serão localizadas numa faixa. O método da sub e sobre-soluções irá desempenhar aqui um papel importante e, combinado com outras ferramentas como a condição unilateral de Nagumo, as funções de Green ou o teorema de ponto fixo de Schauder, fornecem a existência e localização de soluções para equações diferenciais com diversas condições de fronteira. Apresentam-se também diferentes aplicações a fenómenos reais, a maioria deles traduzidos para equações clássicas como as equações de Duffing, Bernoulli-Euler-v.Karman, Fisher-Kolmogorov, Swift - Hohenberg, Emden-Fowler ou ainda Falkner-Skan. Todas estas aplicações têm um denominador comum: são definidas em intervalos ilimitados e os resultados existentes na literatura são raros ou estão provados apenas numericamente em problemas discretos.

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34

Al-Kharafi, Abdulmohsen A. H. "Finite element solution of initial/boundary value problems." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/32335.

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In the last few decades, the Finite Element Method (F.E.M.) has become one of the best techniques used to solve a vast variety of the world's initial/boundary value problems. When such a powerful method is facilitated by a 'user friendly' computer program that possess both pre- and post-processors together with an automatic mesh generation and refinement processor, it becomes indeed a powerful tool to solve a wide range of problems in Applied Mathematics and Engineering. This thesis is an attempt to show the potential of the method which is implemented by a general purpose program used to solve problems governed by partial differential equations (P.D.E.s).

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35

Cossio, Jorge Ivan. "Multiple solutions for semilinear elliptic boundary value problems." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc332487/.

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In this paper results concerning a semilinear elliptic boundary value problem are proven. This problem has five solutions when the range of the derivative of the nonlinearity ƒ includes the first two eigenvalues. The existence and multiplicity or radially symmetric solutions under suitable conditions on the nonlinearity when Ω is a ball in R^N.

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36

Cameron, Seth Andrew 1967. "Novel Fourier methods for biomagnetic boundary value problems." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/278738.

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A novel Fourier technique for solving a wide variety of boundary value problems is introduced. The technique, called Fourier projection, is based on the geometric properties of vector calculus operators in reciprocal space. Fourier projection decomposes arbitrary vector fields into collections of irrotational and/or divergenceless dipole subfields. For well-posed problems, Fourier projection algorithms can calculate unknown field values from a knowledge of primary sources and boundary conditions. Specifically, this technique is applied to several problems associated with biomagnetic imaging, including volume current calculations and equivalent surface current solutions. In addition, a low-cost magnetic field mapping system designed to aid reconstruction algorithm development is described.

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37

Traytak, Sergey D. "Boundary-value problems for the diffusion equation in domains with disconnected boundary." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-195662.

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38

Kapanadze, David, and Bert-Wolfgang Schulze. "Boundary value problems on manifolds with exits to infinity." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2572/.

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We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we prove an analogue of the Atiyah-Bott condition.

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39

Oliaro, Alessandro, and Bert-Wolfgang Schulze. "Parameter-dependent boundary value problems on manifolds with edges." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2642/.

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As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conormal symbols in terms of a calculus of holomorphic parameter-dependent edge boundary value problems on the base. We show that a certain kernel cut-off procedure generates all such holomorphic families, modulo smoothing elements, and we establish conormal symbols as an algebra as is necessary for a parametrix constructions in the elliptic case.

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40

Krainer, Thomas, and Bert-Wolfgang Schulze. "The conormal symbolic structure of corner boundary value problems." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2666/.

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Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.

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41

Qin, Jingsheng. "Initial boundary value problems associated with a spinning string." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq23465.pdf.

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42

Khan, Mohammad Salim. "Finite-difference solutions of fifth-order boundary-value problems." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239268.

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43

Akbar, M. M. "Boundary-value problems in quantum gravity and classical solutions." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595407.

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It is proved that Taub-Bolt infillings are double-valued whereas Taub-Nut and Eguchi-Hanson infillings are unique in arbitrary dimensions. In the case of trivial bundles, there are two or no Schwarzschild infillings. The condition of whether a particular type of infilling exists can be expressed as a limitation on squashing through a functional dependence on dimension in each case. The case of the Eguchi-Hanson metric is solved in arbitrary dimension. The Taub-Nut and the Taub-Bolt are solved in four dimensions and methods for higher dimensions are discussed. For the case of Schwarzschild in arbitrary dimension, thermodynamic properties of the two infilling black-hole solutions are discussed and analytic formulae for their masses are obtained using higher order hypergeometric functions. Convexity of the infilling solutions and isoperimetric inequalities involving the volume of the boundary and the volume of the infilling solutions are investigated. In particular, analogues of Minkowski’s celebrated inequality in flat space are found and discussed. In Chapters 3, the Dirichlet problem is studied for an SU (2) x U(1)-invariant S³ boundary within the class of self-dual Taub-Nut-(anti) de Sitter metrics. Including complex ones there can be a total of three solutions for the infilling although there will be a unique real solution or no real solution depending on the boundary data - the two radii of the S³. Exact solutions of the infilling geometries are obtained making its possible to find their Euclidean actions as analytic functions of the two radii of the S³-boundary. The case of L < 0 is investigated further. For reasonable squashing of the S³, all three infilling solutions have real-valued actions which possess a “cusp catastrophe” structure with a “catastrophe manifold” that shows that the unique real positive-definite solution dominates. The necessary and sufficient condition for the existence of the positive-definite solution is found as a condition on the two radii of the S³. In Chapter 4, the same boundary-value problem is studied for the Taub-Bolt-anti-de Sitter metrics. Such metrics are obtained from the two-parameter Taub-NUT-anti de Sitter family. The condition of regularity results in two bifurcated one-parameter family. It is found that any axially symmetric S³-boundary can be filled in with at least one solution coming from each of these two branches. The infillings appear or disappear catastrophically in pairs as the values of the two radii of S³ are varied; this happens simultaneously for both branches. It is found that the total number in independent infillings is two, six or ten. When the two radii are of the same order and large this number is two. In the isotropic limit, i.e., for round S³ this holds for small radii as well. In Chapter 5, the Dirichlet problem is studied within Euclideanised Schwarzschild-anti de Sitter and anti de Sitter metrics, i.e., for an S¹ x Sⁿ boundary. For such boundary data there exist two or no black-holes and always a unique anti de Sitter solution. The black holes have strictly positive and negative specific heats (and hence locally thermodynamically stable and unstable respectively). It is shown that for any radius of the cavity, the larger hole can be globally thermodynamically stable above a critical temperature by demonstrating that a phase transition occurs from hot AdS to Schwarzschild-AdS within the cavity. This gives the Hawking-Page phase transition in the infinite cavity limit. It is found that the case of five dimensions is special in that the masses of the two black holes, and hence other quantities of classical and semi-classical interest, can be obtained exactly as functions of cavity radius and temperature. It is also possible in this case to obtain the minimum temperature (below which no black holes exist) and the critical temperature for phase transition as analytic functions of cavity-radius. In Chapter 6, cosmological and instanton solutions are found for CP¹ and CP² sigma models coupled to gravity with a possible cosmological constant.

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44

Siddiqui, Aijaz Ahmad. "Finite-difference solutions of tenth-order boundary-value problems." Thesis, Brunel University, 1994. http://bura.brunel.ac.uk/handle/2438/7117.

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In this thesis finite difference methods are used to obtain numerical solutions for a class of high-order ordinary differential equations with applications to eigenvalue problems. Two families of numerical methods are developed for tenth-order boundary-value problems and global extrapolations on two and three grids are considered for the special problem. Special nonlinear tenth-order boundary-value problems are solved using a family of direct finite difference methods which are adapted to solve a general linear and nonlinear boundary-value problem. These methods convert the ordinary differential equation into a set of algebraic equations. If the original ordinary differential equations are linear, the finite difference equations will give linear algebraic equations. If the ordinary differential equation are nonlinear, the resulting finite difference equations will be nonlinear algebraic equations. These nonlinear equations are first linearized by Newton's method. The methods developed are of orders two, four, six, eight, ten and twelve. The error analyses are discussed. A generalized form is given to solve a class of high-order boundary-value problems by converting the differential equation to a system of first-order equations. The method based on using a Pade rational approximant to the exponential function for general boundary-value problems is applied to a tenth-order eigenvalue problem associated with instability in a Benard layer and numerical results are compared with asymtotic estimates appearing in the literature. This method may be implernented on a parallel computer. The method is extended to a twelfth-order eigenvalue problern in an appendix. The algorithms developed are tested on a variety of problems from the literature. The REDUCE package is used to obtain the parameters in the numerical methods and all computations are carried out on a Sun Workstation at Brunel University using Fortran 77 with double precision arithmetic.

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Hummel, Felix Benjamin [Verfasser]. "Stochastic Transmission and Boundary Value Problems / Felix Benjamin Hummel." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1189067293/34.

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46

Nagar, Atulya Kumar. "Application of functional bounds to nonlinear boundary value problems." Thesis, University of York, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318245.

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47

Li, Shenghao. "Non-homogeneous Boundary Value Problems for Boussinesq-type Equations." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1468512590.

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48

Rockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.

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In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the global relation for the Laplace equation on domains with smooth boundary. Using properties of the F_p-transform, we show that the global relation defines a continuously invertible map between the Dirichlet and Neumann data for a given BVP for the Laplace equation. Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.

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49

Eidenschink, Michael. "A comparison of numerical methods for the solution of two-point boundary value problems." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/29224.

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50

Wintz, Nick. "Eigenvalue comparisons for an impulsive boundary value problem with Sturm-Liouville boundary conditions." Huntington, WV : [Marshall University Libraries], 2004. http://www.marshall.edu/etd/descript.asp?ref=414.

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Dissertations / Theses on the topic 'Conjugate boundary value problems'

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