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Academic literature on the topic 'PERTURBED PROBLEM'

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Published: 11 September 2023

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Journal articles on the topic "PERTURBED PROBLEM"

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Vrábeľ, Róbert. "Quasilinear and quadratic singularly perturbed Neumann's problem." Mathematica Bohemica 123, no. 4 (1998): 405–10. http://dx.doi.org/10.21136/mb.1998.125970.

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Yarka, Ulyana, Solomiia Fedushko, and Peter Veselý. "The Dirichlet Problem for the Perturbed Elliptic Equation." Mathematics 8, no. 12 (November 25, 2020): 2108. http://dx.doi.org/10.3390/math8122108.

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In this paper, the authors consider the construction of one class of perturbed problems to the Dirichlet problem for the elliptic equation. The operators of both problems are isospectral, which makes it possible to construct solutions to the perturbed problem using the Fourier method. This article focuses on the Dirichlet problem for the elliptic equation perturbed by the selected variable. We established the spectral properties of the perturbed operator. In this work, we found the eigenvalues and eigenfunctions of the perturbed task operator. Further, we proved the completeness, minimal spanning system, and Riesz basis system of eigenfunctions of the perturbed operator. Finally, we proved the theorem on the existence and uniqueness of the solution to the boundary value problem for a perturbed elliptic equation.
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Nurgabyl, D. N., and S. S. Nazhim. "Recovery problem for a singularly perturbed differential equation with an initial jump." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 100, no. 4 (December 30, 2020): 125–35. http://dx.doi.org/10.31489/2020m4/125-135.

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The article investigates the asymptotic behavior of the solution to reconstructing the boundary conditions and the right-hand side for second-order differential equations with a small parameter at the highest derivative, which have an initial jump. Asymptotic estimates of the solution of the reconstruction problem are obtained for singularly perturbed second-order equations with an initial jump. The rules for the restoration of boundary conditions and the right parts of the original and degenerate problems are established. The asymptotic estimates of the solution of the perturbed problem are determined as well as the difference between the solution of the degenerate problem and the solution of the perturbed problem. A theorem on the existence, uniqueness, and representation of a solution to the reconstruction problem from the position of singularly perturbed equations is proved. The results obtained open up possibilities for the further development of the theory of singularly perturbed boundary value problems for ordinary differential equations.
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Vrbik, Jan. "Two-body perturbed problem revisited." Canadian Journal of Physics 73, no. 3-4 (March 1, 1995): 193–98. http://dx.doi.org/10.1139/p95-027.

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Quaternion formulation of a perturbed two-body problem is extended to include nonconservative forces, and the resulting algorithm is demonstrated using the classical example of the precession of apses.
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Gekeler, E. W. "On the Perturbed Eigenvalue Problem." Journal of Mathematical Analysis and Applications 191, no. 3 (May 1995): 540–46. http://dx.doi.org/10.1006/jmaa.1995.1147.

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6

Vrábeľ, Róbert. "Upper and lower solutions for singularly perturbed semilinear Neumann's problem." Mathematica Bohemica 122, no. 2 (1997): 175–80. http://dx.doi.org/10.21136/mb.1997.125912.

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7

Akmatov, A. "The Regularization Method of Solutions a Bisingularly Perturbed Problem in the Generalized Functions Space." Bulletin of Science and Practice 8, no. 2 (February 15, 2022): 10–17. http://dx.doi.org/10.33619/2414-2948/75/01.

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When singularly perturbed problems are investigated, in the case of a change in stability, all work was performed in the space of analytical functions. Naturally, questions will arise whether it is possible to obtain an estimate of solutions to a singularly perturbed problem without moving to the complex plane. In the work, the first results obtained are the solutions of the singularly motivated task, not moving into the complex plane. For this purpose, a method of regularization in the space of generalized functions has been developed and corresponding estimates have been obtained. If we choose the starting point in a stable interval, then up to the transition point, the asymptotic proximity of solutions to the perturbed and undisturbed problem is in the order of a small parameter ε. The problem will appear when the point belongs to an unstable interval. Therefore, prior to this, the works moved to the complex plane. In such problems, there is a concept of the delay time of solutions to the perturbed and undisturbed problem. Level lines will appear in complex planes. In such problems, there is a concept of the delay time of solutions to the perturbed and undisturbed problem. Level lines will appear in complex planes. At special points, these lines have critical level lines. Therefore, it is impossible to choose the starting point so as to get the maximum delay time. But the asymptotic proximity of solutions of perturbed and undisturbed problems is possible with limited time delays. If we study the solution in the space of generalized functions, then we can choose the starting point with the maximum time delay. And also, without passing to the complex plane, it is possible to establish the asymptotic proximity of solutions to the perturbed and undisturbed problem. For this purpose, a method of regularization of solutions of a singularly perturbed problem has been developed for the first time.
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Han, Xinli, and Lijun Pan. "The Perturbed Riemann Problem with Delta Shock for a Hyperbolic System." Advances in Mathematical Physics 2018 (September 5, 2018): 1–11. http://dx.doi.org/10.1155/2018/4925957.

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In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock. The solutions to the problem are obtained constructively. From the solutions, we see that a delta shock in the corresponding Riemann solution may turn into a shock and a contact discontinuity under a perturbation of the Riemann initial data. This shows the instability and the internal mechanism of a delta shock. Furthermore, we find that the Riemann solution of the hyperbolic system is instable under this perturbation, which is also quite different from the previous perturbed Riemann problems.
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PERJAN, ANDREI, and GALINA RUSU. "Two parameter singular perturbation problems for sine-Gordon type equations." Carpathian Journal of Mathematics 38, no. 1 (November 15, 2021): 201–15. http://dx.doi.org/10.37193/cjm.2022.01.16.

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In the real Sobolev space $H_0^1(\Omega)$ we consider the Cauchy-Dirichlet problem for sine-Gordon type equation with strongly elliptic operators and two small parameters. Using some {\it a priori} estimates of solutions to the perturbed problem and a relationship between solutions in the linear case, we establish convergence estimates for the difference of solutions to the perturbed and corresponding unperturbed problems. We obtain that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of $t=0.$
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PERJAN, ANDREI, and GALINA RUSU. "Abstract linear second order differential equations with two small parameters and depending on time operators." Carpathian Journal of Mathematics 33, no. 2 (2017): 233–46. http://dx.doi.org/10.37193/cjm.2017.02.10.

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In a real Hilbert space H consider the following singularly perturbed Cauchy problem. We study the behavior of solutions uεδ to this problem in two different cases: ε → 0 and δ ≥ δ0 > 0; ε → 0 and δ → 0, relative to solution to the corresponding unperturbed problem. We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0. We show the boundary layer and boundary layer function in both cases.
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Dissertations / Theses on the topic "PERTURBED PROBLEM"

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Nguyen, Thi Phong. "Direct and inverse solvers for scattering problems from locally perturbed infinite periodic layers." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX004/document.

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Nous sommes intéressés dans cette thèse par l'analyse de la diffraction directe et inverse des ondes par des couches infinies périodiques localement perturbées à une fréquence fixe. Ce problème a des connexions avec le contrôle non destructif des structures périodiques telles que des structures photoniques, des fibres optiques, des réseaux, etc. Nous analysons d'abord le problème direct et établissons certaines conditions sur l'indice de réfraction pour lesquelles il n'existe pas de modes guidés. Ce type de résultat est important car il montre les cas pour lesquels les mesures peuvent être effectuées par exemple sur une couche au dessus de la structure périodique sans perdre des informations importantes dans la partie propagative de l'onde. Nous proposons ensuite une méthode numérique pour résoudre le problème de diffraction basée sur l'utilisation de la transformée de Floquet-Bloch dans les directions de périodicité. Nous discrétisons le problème de manière uniforme dans la variable de Floquet-Bloch et utilisons une méthode spectrale dans la discrétisation spatiale. La discrétisation en espace exploite une reformulation volumétrique du problème dans une cellule (équation intégrale de Lippmann-Schwinger) et une périodisation du noyau dans la direction perpendiculaire à la périodicité. Cette dernière transformation permet d'utiliser des techniques de type FFT pour accélérer le produit matrice-vecteur dans une méthode itérative pour résoudre le système linéaire. On aboutit à un système d'équations intégrales couplées (à cause de la perturbation locale) qui peuvent être résolues en utilisant une décomposition de Jacobi. L'analyse de la convergence est faite seulement dans le cas avec absorption et la validation numérique est réalisées sur des exemples 2D. Pour le problème inverse, nous étendons l'utilisation de trois méthodes d'échantillonnage pour résoudre le problème de la reconstruction de la géométrie du défaut à partir de la connaissance de données mutistatiques associées à des ondes incidentes planes en champ proche (c.à.d incluant certains modes évanescents). Nous analysons ces méthodes pour le problème semi-discrétisée dans la variable Floquet-Bloch. Nous proposons ensuite une nouvelle méthode d'imagerie capable de visualiser directement la géométrie du défaut sans savoir ni les propriétés physiques du milieux périodique, ni les propriétés physiques du défaut. Cette méthode que l'on appelle imagerie-différentielle est basée sur l'analyse des méthodes d'échantillonnage pour un seul mode de Floquet-Bloch et la relation avec les solutions de problèmes de transmission intérieurs d'un type nouveau. Les études théoriques sont corroborées par des expérimentations numériques sur des données synthétiques. Notre analyse est faite d'abord pour l'équation d'onde scalaire où le contraste est sur le terme d'ordre inférieur de l'opérateur de Helmholtz. Nous esquissons ensuite l'extension aux cas où la le contraste est également présent dans l'opérateur principal. Nous complémentons notre travail par deux résultats sur l'analyse du problème de diffraction pour des matériaux périodiques ayant des indices négatifs. Nous établissons en premier le caractère bien posé du problème en 2D dans le cas d'un contraste est égal à -1. Nous montrons également le caractère Fredholm de la formulation Lipmann-Schwinger du problème en utilisant l'approche de T-coercivité dans le cas d'un contraste différent de -1
We are interested in this thesis by the analysis of scattering and inverse scattering problems for locally perturbed periodic infinite layers at a fixed frequency. This problem has connexions with non destructive testings of periodic media like photonics structures, optical fibers, gratings, etc. We first analyze the forward scattering problem and establish some conditions under which there exist no guided modes. This type of conditions is important as it shows that measurements can be done on a layer above the structure without loosing substantial informations in the propagative part of the wave. We then propose a numerical method that solves the direct scattering problem based on Floquet-Bloch transform in the periodicity directions of the background media. We discretize the problem uniformly in the Floquet-Bloch variable and use a spectral method in the space variable. The discretization in space exploits a volumetric reformulation of the problem in a cell (Lippmann-Schwinger integral equation) and a periodization of the kernel in the direction orthogonal to the periodicity. The latter allows the use of FFT techniques to speed up Matrix-Vector product in an iterative to solve the linear system. One ends up with a system of coupled integral equations that can be solved using a Jacobi decomposition. The convergence analysis is done for the case with absorption and numerical validating results are conducted in 2D. For the inverse problem we extend the use of three sampling methods to solve the problem of retrieving the defect from the knowledge of mutistatic data associated with incident near field plane waves. We analyze these methods for the semi-discretized problem in the Floquet-Bloch variable. We then propose a new method capable of retrieving directly the defect without knowing either the background material properties nor the defect properties. This so-called differential-imaging functional that we propose is based on the analysis of sampling methods for a single Floquet-Bloch mode and the relation with solutions toso-called interior transmission problems. The theoretical investigations are corroborated with numerical experiments on synthetic data. Our analysis is done first for the scalar wave equation where the contrast is the lower order term of the Helmholtz operator. We then sketch the extension to the cases where the contrast is also present in the main operator. We complement our thesis with two results on the analysis of the scattering problem for periodic materials with negative indices. Weestablish the well posedness of the problem in 2D in the case of a contrast equals -1. We also show the Fredholm properties of the volume potential formulation of the problem using the T-coercivity approach in the case of a contrast different from -1
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Kunert, Gerd. "Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100011.

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Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter. The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well. A numerical example supports the analysis of our anisotropic error estimator.
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Kunert, Gerd. "A note on the energy norm for a singularly perturbed model problem." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100062.

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A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.
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Robert, Kieran Jean-Baptiste. "New approach to solving a spectral problem in a perturbed periodic waveguide." Thesis, Cardiff University, 2008. http://orca.cf.ac.uk/54692/.

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This thesis presents a numerical investigation of a problem on a semi infinite waveguide. The domain considered here is of a much more general form than those that have been considered using classical techniques. The motivation for this work originates from the work in 28, where unlike here, a perturbation technique was used to solve a simpler problem.
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Adkins, Jacob. "A Robust Numerical Method for a Singularly Perturbed Nonlinear Initial Value Problem." Kent State University Honors College / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1513331499579714.

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Grosman, Serguei. "Robust local problem error estimation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600475.

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. An estimator that has shown to be one of the most reliable for reaction-diffusion problem is the equilibrated residual method and its modification done by Ainsworth and Babuška for singularly perturbed problem. However, even the modified method is not robust in the case of anisotropic meshes. The present work modifies the equilibrated residual method for anisotropic meshes. The resulting error estimator is equivalent to the equilibrated residual method in the case of isotropic meshes and is proved to be robust on anisotropic meshes as well. A numerical example confirms the theory.
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Kunert, Gerd. "A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100730.

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The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three modifications of these estimators are introduced and discussed. Numerical experiments for all estimators complement and confirm the theoretical results.
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FUSE', ALESSANDRA. "ON THE STABILITY OF THE PERTURBED CENTRAL MOTION PROBLEM: A QUASICONVEXITY AND A NEKHOROSHEV TYPE RESULT." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/565234.

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The aim of this thesis is the study of the dynamics of small perturbations of the spatial central motion problem. Our main result consists in proving that if the central potential is analytic, then, except for the Harmonic and the Keplerian case, the unperturbed system written in action angle variables is quasiconvex. Thus, when it is perturbed, one can apply a Nekhoroshev type theorem ensuring the stability over exponentially long times of the modulus of the angular momentum and of the energy of the unperturbed system. Being a \emph{superintegrable} system, namely, a system which admits a number of independent integrals of motion larger than the number of degrees of freedom, the version of Nekhoroshev theorem provided here is the one for superintegrable systems. We also give a complete proof (à la Lochak) of this result.
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Dalla, Riva Matteo. "Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426270.

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The dissertation is made of two chapters. The first chapter is dedicated to the investigation of some properties of the layer potentials of a constant coefficient elliptic partial differential operator. In the second chapter, we focus our attention to the Lamè equations, which are related to the physic of an isotropic homogeneous elastic body. In particular, in the first chapter, we investigate the dependence of the single layer potential upon perturbation of the density, the support and the coefficients of the corresponding operator. Under some more restrictive assumptions on the operator, we prove a real analyticity theorem for the single layer potential and its derivatives. As a first step, we introduce a particular fundamental solution of a given constant coefficient partial differential operator. For this purpose, we exploite the construction of a fundamental solution given by John (1955). We have verified that, if the coefficients of the operator are constrained to a bounded set, then there exist a particular fundamental solution which is a sum of functions which depend real analytically on the coefficients of the operator. Such a result resembles the results of Mantlik (1991, 1992) (see also Tréves (1962)), where more general assumptions on the operator are considered. We observe that it is not a corollary. Indeed, we need a suitably detailed expression for the fundamental solution, which cannot be deduced by Mantlik's results. The next step is to introduce the support of our single layer potentials. It will be a compact sub-manifold of the the n-dimensional euclidean space parametrized by a suitable diffeomorphism defined on the boundary of a fixed domain. Then, we will be ready to state in Theorem 1.7 the main result of this chapter, which is a real analyticity result in the frame of Shauder spaces. The main idea of the proof stems from the papers of Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005) and exploits the Implicit Mapping Theorem for real analytic functions. Indeed, our main Theorem 1.7 is in some sense a natural extension of theorems obtained by Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005), for the Cauchy integral and for the Laplace and Helmholtz operators, respectively. Here we confine our attention to elliptic operators which can be factorized with operators of order 2. In the last section of the first chapter, we consider some applications of Theorem 1.7. In particular, we deduce a real analyticity theorem for the single and double layer potential which arise in the analysis of the boundary value problems for the Lamè equations and for the Stokes system. In the second chapter, we focus our attention to the Lamè equations. We consider some boundary value problems defined in a domain with a small hole. For each of them, we investigate the behavior of the solution and of the corresponding energy integral as the hole shrinks to a point. This kind of problem is not new at all and has been long investigated by the techniques of asymptotic analysis. It is perhaps difficult to give a complete list of contributions. Here we mention the work of Keller, Kozlov, Movchan, Maz'ya, Nazarov, Plamenewskii, Ozawa and Ward. The results that we present are in accordance with the behavior one would expect by looking at the above mentioned literature, but we adopt a different approach proposed by Lanza de Cristoforis (2001, 2002, 2005, 2007.) To do so, we exploit the real analyticity results for the elastic layer potentials obtained in the first chapter. We now briefly outline the main difference between our approach and the one of asymptotic analysis. Let d>0 be a parameter which is proportional to the diameter of the hole, so that the singularity of the domain appears when d=0. By the approach of the asymptotic analysis, we can expect to obtain results which are expressed by means of known functions of d plus an unknown term which is smaller than a positive power of d. Whereas, our results are expressed by means of real analytic functions of d defined in a whole open neighborhood of d=0 and by, possibly singular, but completely known functions of d, such as d^(2-n) or log d. Moreover, not only we can consider the dependence upon d, we can also investigate the dependence of the solution and the corresponding energy integral upon perturbations of the coefficients of the operator, and of the point where the hole is situated, and of the shape of the hole, and of the shape of the outer domain, and of the boundary data on the boundary of the hole, and of the boundary data on the boundary of the outer domain, and of the interior data. Also in this case we obtain results expressed by means of real analytic functions and completely known functions such as d^(2-n) and log d. The first boundary value problem we have studied is a Dirichlet boundary value problem with homogeneous data in the interior. Then, we turned to investigate a Robin boundary value problem with homogeneous data in the interior. In this case we have also described the behavior of the solution and the corresponding energy integral when both the domain and the boundary data display a singularity for d=0. Finally, we have studied a Dirichlet boundary value problem with non-homogeneous data in the interior.
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Zhang, Ningyi. "Inverse problem for wave propagation in a perturbed layered half-space and orthogonality relations in poroelastic materials." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 120 p, 2007. http://proquest.umi.com/pqdweb?did=1342733281&sid=1&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Books on the topic "PERTURBED PROBLEM"

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Boglaev, Igor. Domain decomposition in boundary layers for a singularly perturbed parabolic problem. Palmerston North, N.Z: Faculty of Information and Mathematical Sciences, Massey University, 1997.

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Dalla Riva, Matteo, Massimo Lanza de Cristoforis, and Paolo Musolino. Singularly Perturbed Boundary Value Problems. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76259-9.

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Barbu, Luminiţa, and Gheorghe Moroşanu. Singularly Perturbed Boundary-Value Problems. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8331-2.

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Gheorghe, Moroșanu, ed. Singularly perturbed boundary-value problems. Basel, Switzerland: Birkhäuser Verlag, 2007.

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Weak convergence methods and singularly perturbed stochastic control and filtering problems. Boston: Birkhäuser, 1990.

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Kushner, Harold J. Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-4482-0.

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Maz’ya, Vladimir, Serguei Nazarov, and Boris A. Plamenevskij. Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8432-7.

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Maz’ya, Vladimir, Serguei Nazarov, and Boris A. Plamenevskij. Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8434-1.

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Mazia, V. G. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Basel: Springer Basel, 2000.

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Mazʹi︠a︡, V. G. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Basel: Birkhäuser Verlag, 2000.

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Book chapters on the topic "PERTURBED PROBLEM"

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Rummel, C., H. Hofmann, and J. Ankerhold. "Extensions of the Perturbed SPA." In The Nuclear Many-Body Problem 2001, 215–22. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0460-2_30.

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Dalla Riva, Matteo, Massimo Lanza de Cristoforis, and Paolo Musolino. "A Dirichlet Problem in a Domain with Two Small Holes." In Singularly Perturbed Boundary Value Problems, 373–431. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76259-9_10.

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Dalla Riva, Matteo, Massimo Lanza de Cristoforis, and Paolo Musolino. "A Dirichlet Problem in a Domain with a Small Hole." In Singularly Perturbed Boundary Value Problems, 261–335. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76259-9_8.

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Wasow, Wolfgang. "A Singularly Perturbed Turning Point Problem." In Linear Turning Point Theory, 197–214. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-1090-0_11.

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Deuring, Paul. "Resolvent Estimates for a Perturbed Oseen Problem." In Functional Analysis and Evolution Equations, 171–86. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7794-6_11.

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Kushner, Harold J. "The Nonlinear Filtering Problem." In Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems, 115–50. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-4482-0_6.

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Cai, Chenxiao, Zidong Wang, Jing Xu, and Yun Zou. "The Sensitivity-Shaping Problem for Singularly Perturbed Systems." In Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems, 137–77. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45405-4_6.

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Salmon, G., J. J. Strodiot, and V. H. Nguyen. "A Perturbed Auxiliary Problem Method for Paramonotone Multivalued Mappings." In Nonconvex Optimization and Its Applications, 515–29. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0279-7_33.

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Banasiak, Jacek, and Mirosław Lachowicz. "Asymptotic Expansion Method in a Singularly Perturbed McKendrick Problem." In Methods of Small Parameter in Mathematical Biology, 143–72. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05140-6_5.

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Rai, Pratima, and Kapil K. Sharma. "Singularly Perturbed Convection-Diffusion Turning Point Problem with Shifts." In Mathematical Analysis and its Applications, 381–91. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_31.

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Conference papers on the topic "PERTURBED PROBLEM"

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Armellin, Roberto, David Gondelach, and Juan Felix San Juan. "Multi-revolution perturbed Lambert problem." In 2018 Space Flight Mechanics Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-1968.

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Tokmagambetov, Niyaz, and Gulzat Nalzhupbayeva. "Operator perturbed Cauchy problem for the Gellerstedt equation." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930524.

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Dalla Riva, M., and M. Lanza de Cristoforis. "Singularly perturbed loads for a nonlinear traction boundary value problem on a singularly perturbed domain." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0004.

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"Asymptotics of solving a singularly perturbed boundary value problem." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.136.

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Vedula, Lalit, and N. Sri Namachchivaya. "Stochastically Perturbed Rotating Shafts." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21450.

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Abstract:
Abstract The objective of this work is to study the long term effects of small symmetry-breaking, dissipative and noisy perturbations on the dynamics of a rotating shaft. Hamilton’s principle is used to derive the equations of motion and a one mode Galerkin approximation is applied to obtain a two-degree-of-freedom (four dimensional) model. A stochastic averaging method is developed to reduce the dimension of this four dimensional system. Making use of the interaction between the gyroscopic and dissipative forces and the separation of time scales, the original system is reduced to a one dimensional Markov process. Depending on the system parameters, the reduced Markov process takes its values on a line or a graph. For the latter case, the glueing conditions required to complete the description of the problem in the reduced space are derived. This provides a qualitatively accurate and computationally feasible description of the system. Analytical results are obtained for the mean first passage time problem. The stationary probability density is obtained by solving the Fokker Planck Equation (FPE). Finally, the qualitative changes in the stationary density as a result of varying the system parameters are described.
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Myshkov, Stanislav K., and Vladimir V. Karelin. "Minimax control in the singularly perturbed linear-quadratic stabilization problem." In 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP). IEEE, 2015. http://dx.doi.org/10.1109/scp.2015.7342130.

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Zhao, Yali, Qian Zhang, and Shuyi Zhang. "Perturbed Iterative Algorithms for Split General Mixed Variational Inequality Problem." In 2017 International Conference on Applied Mathematics, Modeling and Simulation (AMMS 2017). Paris, France: Atlantis Press, 2017. http://dx.doi.org/10.2991/amms-17.2017.9.

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Sobolev, Vladimir. "Decomposition of Traveling Wave Existence Problem for Singularly Perturbed Equations." In 2020 International Conference on Information Technology and Nanotechnology (ITNT). IEEE, 2020. http://dx.doi.org/10.1109/itnt49337.2020.9253204.

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BOGLAEV, IGOR. "FINITE DIFFERENCE DOMAIN DECOMPOSITION FOR A SINGULARLY PERTURBED PARABOLIC PROBLEM." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0050.

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Kuznetsov, Evgenii, Sergey Leonov, and Katherine Tsapko. "On the exact solution of a singularly perturbed aerodynamic problem." In COMPUTATIONAL MECHANICS AND MODERN APPLIED SOFTWARE SYSTEMS (CMMASS’2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135674.

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Reports on the topic "PERTURBED PROBLEM"

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Ferguson, Warren E., and Jr. Analysis of a Singularly-Perturbed Linear Two-Point Boundary-Value Problem. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada172582.

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Garbey, M., and H. G. Kaper. Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems. Office of Scientific and Technical Information (OSTI), April 1995. http://dx.doi.org/10.2172/510563.

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Kushner, Harold J. Functional Occupation Measures and Ergodic Cost Problems for Singularly Perturbed Stochastic Systems. Fort Belvoir, VA: Defense Technical Information Center, April 1989. http://dx.doi.org/10.21236/ada208578.

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Adjerid, Slimane, Mohammed Aiffa, and Joseph E. Flaherty. High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada290410.

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Flaherty, Joseph E., and Robert E. O'Malley. Asymptotic and Numerical Methods for Singularly Perturbed Differential Equations with Applications to Impact Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada169251.

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