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Keywords:
limit behavior of solutions; existence; uniqueness; equivalued surface; equivalued interface; hyperbolic equation
Summary:
This paper deals with a kind of hyperbolic boundary value problems with equivalued surface on a domain with thin layer. Existence and uniqueness of solutions are given, and the limit behavior of solutions is studied in this paper.
References:
[1] Brezis, H.: Analyse Fonctionnelle. Théorie et Applications. Masson Paris (1993), French. MR 0697382
[2] Chen, Y.: Second Order Parabolic Differential Equations. Peking University Press Beijing (2003), Chinese.
[3] Damlamian, A., Ta-tsien Li: Comportements limites des solutions de certains probl\`emes mixtes pour des équations hyperboliques linéaires. Commun. Partial Differ. Equations 7 (1982), 117-139 French. DOI 10.1080/03605308208820219 | MR 0646133 | Zbl 0504.35052
[4] DiBenedetto, E.: Degenerate Parabolic Equations. Springer New York (1993). MR 1230384 | Zbl 0794.35090
[5] Evans, L. C.: Partial Differential Equations. Graduate Studies in Math. Vol. 19. AMS, American Mathematical Society Providence (1998). MR 1625845
[6] Ladyzhenskaya, O. A.: The Boundary Value Problems of Mathematical Physics. Springer Berlin (1985). MR 0793735 | Zbl 0588.35003
[7] Li, F.: Limit behaviour of solutions to a class of boundary value problem with equivalued surface for hyperbolic equations. Asymptotic Anal. 22 (2000), 163-176. MR 1742533 | Zbl 0946.35046
[8] Ta-tsien Li et al.: Boundary value problems with equivalued surface boundary conditons for self-adjoint elliptic differential equations I, II. Fudan J., Nat. Sci. 1 (1976), 61-71, 136-145 Chinese.
[9] Ta-tsien Li: A class of non-local boundary value problems for partial differential equations and its applications in numerical analysis. J. Comput. Appl. Math. 28 (1989), 49-62. DOI 10.1016/0377-0427(89)90320-8
[10] Ta-tsien Li, Song-mu Zheng, Yong-ji Tan, Wei-xi Shen: Boundary Value Problem with Equivalued Surface and Resistivity Well-Logging. Pitman Research Notes in Math. Series 382. Longman Harlow (1998). MR 1638883
[11] Ta-tsien Li, Yan, J.: Limit behaviour of solutions to certain kinds of boundary value problems with equivalued surface. Asymptotic Anal. 21 (1999), 23-35. MR 1718640 | Zbl 0936.35053
[12] Lions, J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod & Gauthier-Villars Paris (1969), French. MR 0259693 | Zbl 0189.40603
[13] Lions, J.-L., Magenes, E.: Non-Homogeneous Boudary Value Problems and Applications, Vol. II. Springer Berlin (1972). MR 0350178
[14] Zeidler, E.: Nonlinear Functional Analysis and its Applications. II/A: Linear Monotone Operators. Springer New York (1990). MR 1033497 | Zbl 0684.47028
[15] Zhang, H., Wang, X., Zhang, B.: Sound Waves and Acoustic Fields in Boreholes. Science Press Beijing (2004), Chinese.
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