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Journal articles on the topic 'Free Boundary Value Problem'

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Published: 4 June 2021

Last updated: 20 February 2023

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1

Заика, Юрий Васильевич, Наталья Ивановна Родченкова, Yury Zaika, and Natalia Rodchenkova. "Boundary-value problem with free boundary: zirconium alloy hydrogenation." Proceedings of the Karelian Research Centre of the Russian Academy of Sciences, no. 08 (September 1, 2016): 24. http://dx.doi.org/10.17076/mat392.

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2

Fazio, R. "A nonlinear hyperbolic free boundary value problem." Acta Mechanica 81, no. 3-4 (September 1990): 221–26. http://dx.doi.org/10.1007/bf01176989.

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3

Fazio, R. "The Blasius problem formulated as a free boundary value problem." Acta Mechanica 95, no. 1-4 (March 1992): 1–7. http://dx.doi.org/10.1007/bf01170800.

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4

Bauer, Florian, Daniela Kraus, Oliver Roth, and Elias Wegert. "Beurling’s free boundary value problem in conformal geometry." Israel Journal of Mathematics 180, no. 1 (October 31, 2010): 223–53. http://dx.doi.org/10.1007/s11856-010-0102-1.

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5

Ariel, P. D. "Stagnation point flow—a free boundary value problem formulation." International Journal of Computer Mathematics 49, no. 1-2 (January 1993): 123–31. http://dx.doi.org/10.1080/00207169308804222.

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6

Ben Amar, Martine. "Void electromigration as a moving free-boundary value problem." Physica D: Nonlinear Phenomena 134, no. 2 (October 1999): 275–86. http://dx.doi.org/10.1016/s0167-2789(99)00110-4.

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7

Bohé, Adriana. "Free Layers in a Singularly Perturbed Boundary Value Problem." SIAM Journal on Mathematical Analysis 21, no. 5 (September 1990): 1264–80. http://dx.doi.org/10.1137/0521070.

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8

Li, Qingguo, and Shahram Payandeh. "Planning Velocities of Free Sliding Objects as a Free Boundary Value Problem." International Journal of Robotics Research 23, no. 1 (January 2004): 69–87. http://dx.doi.org/10.1177/0278364904036094.

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9

Lee, Donghyun. "Initial value problem for the free-boundary magnetohydrodynamics with zero magnetic boundary condition." Communications in Mathematical Sciences 16, no. 3 (2018): 589–615. http://dx.doi.org/10.4310/cms.2018.v16.n3.a1.

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10

Gröger, K., and N. Strecker. "A Free Boundary Value Problem Modeling Thermal Oxidation of Silicon." Zeitschrift für Analysis und ihre Anwendungen 7, no. 1 (1988): 57–66. http://dx.doi.org/10.4171/zaa/282.

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11

Ang, Dang Ding, Tim Folias, Fritz Keinert, and Frank Stenger. "Viscoplastic flow due to penetration: a free boundary value problem." International Journal of Fracture 39, no. 1-3 (March 1989): 121–27. http://dx.doi.org/10.1007/bf00047445.

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12

Nadirashvili, Nikolai S., and Alexei V. Penskoi. "Free boundary minimal surfaces and overdetermined boundary value problems." Journal d'Analyse Mathématique 141, no. 1 (September 2020): 323–29. http://dx.doi.org/10.1007/s11854-020-0129-0.

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13

Kanakadurga Devi, P., V. G. Naidu, K. Mamatha, and B. Naresh. "Free and Moving Boundary Problems of Heat and Mass Transfer." International Journal of Engineering & Technology 7, no. 3.27 (August 15, 2018): 18. http://dx.doi.org/10.14419/ijet.v7i3.27.17644.

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Bisection method is used to solve a moving boundary problem. This moving boundary problem was solved by the maze of mathematical manipulations by several authors. The method of using bisection is simple as compared to the lengthy mathematical manipulation of other methods. The procedure of the paper is useful in other moving boundary problems of heat and mass transfer, including boundary value problems involving ordinary differential equations with unknown interval length.

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14

Kopachevsky, N. D., and D. O. Tsvetkov. "Small Motions of an Ideal Stratiﬁed Fluid in a Basin Covered with Ice." Contemporary Mathematics. Fundamental Directions 64, no. 3 (December 15, 2018): 573–90. http://dx.doi.org/10.22363/2413-3639-2018-64-3-573-590.

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We study the problem on small motions of an ideal stratiﬁed ﬂuid with a free surface partially covered with crushed ice. The crushed ice is supposed to be ponderable particles of some matter ﬂoating on the free surface. These particles do not interact with each other during oscillations of the free boundary (or this interaction is neglible) and stay on the surface during these oscillations. Using the method of orthogonal projecting of boundary-value conditions on the free surface and introducing auxiliary problems, we reduce the original initial-boundary value problem to the equivalent Cauchy problem for a second-order diﬀerential equation in some Hilbert space. We obtain conditions under which there exists a strong with respect to time solution of the initial-boundary value problem describing the evolution of this hydraulic system.

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15

Kasumba, Henry, Karl Kunisch, and Antoine Laurain. "A bilevel shape optimization problem for the exterior Bernoulli free boundary value problem." Interfaces and Free Boundaries 16, no. 4 (2014): 459–87. http://dx.doi.org/10.4171/ifb/326.

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16

COLIN, THIERRY, and PIERRE FABRIE. "A FREE BOUNDARY PROBLEM MODELING A FOAM DRAINAGE." Mathematical Models and Methods in Applied Sciences 10, no. 06 (August 2000): 945–61. http://dx.doi.org/10.1142/s0218202500000483.

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We study a reaction-diffusion problem with a free boundary governing the evolution of a foam. We show that the problem is globaly well-posed and that the solution converges, when the viscosity tends to zero to the solution of an initial-boundary value problem for Burgers equation.

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17

Guidotti, Patrick. "A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems." Journal of Evolution Equations 2, no. 4 (November 2002): 395–424. http://dx.doi.org/10.1007/pl00012596.

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18

Ying, Wenjun, and Wei-Cheng Wang. "A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs." Communications in Computational Physics 15, no. 4 (April 2014): 1108–40. http://dx.doi.org/10.4208/cicp.170313.071113s.

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AbstractThis work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations (PDEs), including both boundary value and interface problems. The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations. Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution, which satisfies an equivalent discrete interface problem, while the interface problem is solved by a fast solver in the Cartesian grid. The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain. This paper gives implementation details for a second-order version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems. The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem, where the elliptic PDEs on two sides of the interface are of different types.

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19

LIU, LI, and HAIRONG YUAN. "STABILITY OF CYLINDRICAL TRANSONIC SHOCKS FOR THE TWO-DIMENSIONAL STEADY COMPRESSIBLE EULER SYSTEM." Journal of Hyperbolic Differential Equations 05, no. 02 (June 2008): 347–79. http://dx.doi.org/10.1142/s0219891608001519.

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We establish the stability of a class of cylindrical symmetric transonic shocks for two-dimensional complete compressible steady Euler system. This result partly explains the effectiveness of the popular quasi-one-dimensional model of nozzle flows used in aerodynamics. Mathematically, we solve a nonlinear free boundary problem of an elliptic-hyperbolic composite system, with the circular transonic shock front as the free boundary. We accomplish this by finding a (locally) unique fixed point of an appropriately defined boundary profile updating mapping. To define this mapping, we encounter a series of nonclassical boundary value problems in an annulus, which involve a new type of nonlocal elliptic problem, and integral-like solvability conditions to determine the position of the free boundary. This reflects an interesting new feature of boundary value problems of elliptic-hyperbolic composite systems.

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20

Denk, Robert, Matthias Geissert, Matthias Hieber, Jürgen Saal, and Okihiro Sawada. "The Spin-Coating Process: Analysis of the Free Boundary Value Problem." Communications in Partial Differential Equations 36, no. 7 (July 2011): 1145–92. http://dx.doi.org/10.1080/03605302.2010.546469.

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21

Lienstromberg, Christina. "A free boundary value problem modelling microelectromechanical systems with general permittivity." Nonlinear Analysis: Real World Applications 25 (October 2015): 190–218. http://dx.doi.org/10.1016/j.nonrwa.2015.03.008.

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22

Kharab, A., and R. B. Guenther. "A free boundary value problem for water invading an unsaturated medium." Computing 38, no. 3 (September 1987): 185–207. http://dx.doi.org/10.1007/bf02240095.

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23

Kress, Rainer. "On Trefftz’ integral equation for the Bernoulli free boundary value problem." Numerische Mathematik 136, no. 2 (October 26, 2016): 503–22. http://dx.doi.org/10.1007/s00211-016-0847-5.

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24

Witsch, Karl J., and R. Leis. "On a free boundary value problem of physical geodesy, I (uniqueness)." Mathematical Methods in the Applied Sciences 7, no. 1 (1985): 269–89. http://dx.doi.org/10.1002/mma.1670070118.

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25

Witsch, K. J., and R. Leis. "On a free boundary value problem of physical geodesy, II (existence)." Mathematical Methods in the Applied Sciences 8, no. 1 (1986): 1–22. http://dx.doi.org/10.1002/mma.1670080102.

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26

Haddar, Houssem, and Rainer Kress. "A conformal mapping algorithm for the Bernoulli free boundary value problem." Mathematical Methods in the Applied Sciences 39, no. 10 (September 23, 2015): 2477–87. http://dx.doi.org/10.1002/mma.3708.

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27

Oestreich, D. "A New Approach to a Free Boundary Value Problem of Miranda." Mathematische Nachrichten 148, no. 1 (1990): 303–12. http://dx.doi.org/10.1002/mana.3211480120.

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28

ITOH, SHIGEHARU, NAOTO TANAKA, and ATUSI TANI. "ON SOME BOUNDARY VALUE PROBLEM FOR THE STOKES EQUATIONS IN AN INFINITE SECTOR." Analysis and Applications 04, no. 04 (October 2006): 357–75. http://dx.doi.org/10.1142/s0219530506000826.

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As a model problem of the stationary free boundary problem for the Navier–Stokes equations in a vessel whose wall has a contact with a free surface, we are concerned in this paper with the boundary value problem for the stationary Stokes equations in an infinite sector with the slip and the stress boundary conditions. Existence of the unique solution is proved in weighted Sobolev spaces by means of the Mellin transform.

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29

HILDITCH, DAVID. "AN INTRODUCTION TO WELL-POSEDNESS AND FREE-EVOLUTION." International Journal of Modern Physics A 28, no. 22n23 (September 20, 2013): 1340015. http://dx.doi.org/10.1142/s0217751x13400150.

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These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of evolution partial differential equations. I show how strong hyperbolicity guarantees well-posedness of the initial value problem. Symmetric hyperbolic systems are shown to render the initial boundary value problem well-posed with maximally dissipative boundary conditions. I discuss the Laplace–Fourier method for analyzing the initial boundary value problem. Finally, I state how these notions extend to systems that are first-order in time and second-order in space. In the second lecture I discuss the effect that the gauge freedom of electromagnetism has on the PDE status of the initial value problem. I focus on gauge choices, strong-hyperbolicity and the construction of constraint preserving boundary conditions. I show that strongly hyperbolic pure gauges can be used to build strongly hyperbolic formulations. I examine which of these formulations is additionally symmetric hyperbolic and finally demonstrate that the system can be made boundary stable.

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30

Lifits, S. A., S. Yu Reutskiy, G. Pontrelli, and B. Tirozzi. "Quasi Trefftz Spectral Method for Stokes Problem." Mathematical Models and Methods in Applied Sciences 07, no. 08 (December 1997): 1187–212. http://dx.doi.org/10.1142/s021820259700058x.

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A new numerical Quasi Trefftz Spectral Method (QTSM) which was earlier suggested for solving boundary value and initial value problems with elliptic operators is applied to linear stationary hydrodynamic problems. The primitive variables [Formula: see text] are used. The method has been found to work well for different problems, including free boundary ones. The problem of the Stefan type in the domain with moving boundary is also considered. The possibilities of further developments of QTSM are discussed.

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31

Hou, Thomas Y. "Numerical Solutions to Free Boundary Problems." Acta Numerica 4 (January 1995): 335–415. http://dx.doi.org/10.1017/s0962492900002567.

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Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity formation and possible change of topology in the moving free surfaces, and the severe time-stepping stability constraint due to the stiffness of high-order regularisation effects, such as surface tension.This paper reviews some of the recent advances in developing stable and efficient numerical algorithms for solving free boundary-value problems arising from fluid dynamics and materials science. In particular, we will consider boundary integral methods and the level-set approach for water waves, general multi-fluid interfaces, Hele–Shaw cells, crystal growth and solidification. We will also consider the stabilising effect of surface tension and curvature regularisation. The issue of numerical stability and convergence will be discussed, and the related theoretical results for the continuum equations will be addressed. This paper is not intended to be a detailed survey and the discussion is limited by both the taste and expertise of the author.

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32

Chen, Wei. "G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty." Journal of Applied Mathematics 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/910809.

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The target of this paper is to establish the bid-ask pricing framework for the American contingent claims against risky assets with G-asset price systems on the financial market under Knightian uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider bid-ask pricing American contingent claims under Knightian uncertainty, by using G-Dooby-Meyer decomposition; we construct dynamic superhedge strategies for the optimal stopping problem and prove that the value functions of the optimal stopping problems are the bid and ask prices of the American contingent claims under Knightian uncertainty. Finally, we consider a free boundary problem, prove the strong solution existence of the free boundary problem, and derive that the value function of the optimal stopping problem is equivalent to the strong solution to the free boundary problem.

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33

Maekawa, T. "Computation of Shortest Paths on Free-Form Parametric Surfaces." Journal of Mechanical Design 118, no. 4 (December 1, 1996): 499–508. http://dx.doi.org/10.1115/1.2826919.

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Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

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34

Jianfu, Yang. "Remarks on the equilibrium shape of a Tokamak plasma." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 6 (1993): 1059–70. http://dx.doi.org/10.1017/s0308210500029735.

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SynopsisThe equilibrium of a Tokamak plasma not confined inside a conducting shell is governed by a free boundary value problem. The existence of solutions of the free boundary value problem is discussed.

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35

Matthews, John V., and David G. Schaeffer. "A Well-Posed Free Boundary Value Problem for a Hyperbolic Equation with Dirichlet Boundary Conditions." SIAM Journal on Mathematical Analysis 36, no. 1 (January 2004): 256–71. http://dx.doi.org/10.1137/s0036141002408708.

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36

Cannon, John R., and Alec L. Matheson. "A free boundary value problem related to the combustion of a solid: flux boundary conditions." Quarterly of Applied Mathematics 55, no. 4 (December 1, 1997): 687–705. http://dx.doi.org/10.1090/qam/1486543.

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37

Ying, Wenjun, and Craig S. Henriquez. "A kernel-free boundary integral method for elliptic boundary value problems." Journal of Computational Physics 227, no. 2 (December 2007): 1046–74. http://dx.doi.org/10.1016/j.jcp.2007.08.021.

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38

Dewynne, J. N., S. D. Howison, I. Rupf, and P. Wilmott. "Some mathematical results in the pricing of American options." European Journal of Applied Mathematics 4, no. 4 (December 1993): 381–98. http://dx.doi.org/10.1017/s0956792500001194.

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We examine the Black–Scholes partial differential equation for the pricing of a traded option (an American call option on an asset paying a continuous dividend) and make comparisons with other well known free boundary diffusion problems, such as the oxygen consumption problem. The pricing of American options can be viewed as a free boundary problem and is, therefore, inherently nonlinear. We consider the short and long time behaviour of the free boundary, present analytic results for the option value in such limits, and consider the formulation of the problem as a variational inequality, and its numerical solution.

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39

ALEKSEENKO, ALEXANDER M. "WELL-POSED INITIAL-BOUNDARY VALUE PROBLEM FOR A CONSTRAINED EVOLUTION SYSTEM AND RADIATION-CONTROLLING CONSTRAINT-PRESERVING BOUNDARY CONDITIONS." Journal of Hyperbolic Differential Equations 04, no. 04 (December 2007): 587–612. http://dx.doi.org/10.1142/s0219891607001276.

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A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system evolving the constraint quantity statically, i.e. the second time derivative of the constraint quantity is zero. A new set of radiation-controlling constraint-preserving boundary conditions is constructed for the free evolution problem. Comparison between the new conditions and the standard constraint-preserving boundary conditions is made using the Fourier–Laplace analysis and the power series decomposition in time. The new boundary conditions satisfy the Kreiss condition and are free from the ill-posed modes growing polynomially in time.

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40

Lefevere, Anne-Marie. "Singular perturbation of a nonlinear problem with multiple solutions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 100, no. 3-4 (1985): 327–41. http://dx.doi.org/10.1017/s0308210500013858.

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SynopsisA nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().

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41

Bae, Hantaek. "Solvability of the free boundary value problem of the Navier-Stokes equations." Discrete & Continuous Dynamical Systems - A 29, no. 3 (2011): 769–801. http://dx.doi.org/10.3934/dcds.2011.29.769.

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42

Xu, Xiao-Jian. "Free vibration of nonlocal beams: Boundary value problem and a calibration method." Thin-Walled Structures 161 (April 2021): 107423. http://dx.doi.org/10.1016/j.tws.2020.107423.

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43

Cannon, John R., James C. Cavendish, and Antonio Fasano. "A Free Boundary-Value Problem Related to the Combustion of a Solid." SIAM Journal on Applied Mathematics 45, no. 5 (October 1985): 798–809. http://dx.doi.org/10.1137/0145047.

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44

Hilditch, David, and Milton Ruiz. "The initial boundary value problem for free-evolution formulations of general relativity." Classical and Quantum Gravity 35, no. 1 (December 5, 2017): 015006. http://dx.doi.org/10.1088/1361-6382/aa96c6.

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45

Tomi, Friedrich. "A finiteness result in the free boundary value problem for minimal surfaces." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 3, no. 4 (July 1986): 331–43. http://dx.doi.org/10.1016/s0294-1449(16)30383-3.

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46

Ivanyshyn Yaman, Olha, and Rainer Kress. "Nonlinear integral equations for Bernoulli’s free boundary value problem in three dimensions." Computers & Mathematics with Applications 74, no. 11 (December 2017): 2784–91. http://dx.doi.org/10.1016/j.camwa.2017.06.011.

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47

Burman, Erik, Daniel Elfverson, Peter Hansbo, Mats G. Larson, and Karl Larsson. "A cut finite element method for the Bernoulli free boundary value problem." Computer Methods in Applied Mechanics and Engineering 317 (April 2017): 598–618. http://dx.doi.org/10.1016/j.cma.2016.12.021.

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48

Zhen, Wang, and Zhang Hui. "Free boundary value problem of one dimensional two-phase liquid-gas model." Acta Mathematica Scientia 32, no. 1 (January 2012): 413–32. http://dx.doi.org/10.1016/s0252-9602(12)60026-5.

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49

Austen, Gerrit, and Wolfgang Keller. "Singularity free formulations of the geodetic boundary value problem in gravity-space." Journal of Geodesy 83, no. 7 (October 19, 2008): 645–57. http://dx.doi.org/10.1007/s00190-008-0278-x.

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50

Ardalan, Alireza A., Roohollah Karimi, and M. Poutanen. "A bias-free geodetic boundary value problem approach to height datum unification." Journal of Geodesy 84, no. 2 (October 10, 2009): 123–34. http://dx.doi.org/10.1007/s00190-009-0348-8.

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