A method for finding coefficients of a quasilinear hyperbolic equation

被引：0

作者：

Shcheglov A.Y. ^{[1
]}

机构：

[1] Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow

来源：

Computational Mathematics and Mathematical Physics | 2006年 / 46卷 / 5期

基金：

俄罗斯基础研究基金会;

关键词：

Inverse problem for two coefficients; Iteration method; Quasilinear hyperbolic equation;

D O I：

10.1134/S0965542506050058

中图分类号：

学科分类号：

摘要：

The inverse problem of finding the coefficients q(s) and p(s) in the equation u tt = a 2 u xx + q(u)u t - p(u)u x is investigated. As overdetermination required in the inverse setting, two additional conditions are set: a boundary condition and a condition with a fixed value of the timelike variable. An iteration method for solving the inverse problem is proposed based on an equivalent system of integral equations of the second kind. A uniqueness theorem and an existence theorem in a small domain are proved for the inverse problem to substantiate the convergence of the algorithm. © MAIK "Nauka/Interperiodica" (Russia), 2006.

引用

页码：776 / 795

页数：19

共 16 条

[1]

Denisov A.M., Introduction into the Theory of Inverse Problems, (1994)

[2]

Prilepko A.I., Orlovsky D.G., Vasin I.A., Methods for Solving Inverse Problems in Mathematical Physics, (1999)

[3]

Ishmukhametov A.Z., Stability and Approximation of Optimal Control Problem, (2000)

[4]

Iskenderov A.D., On an inverse problem for quasilinear parabolic equations, Differ. Uravn., 10, pp. 890-898, (1974)

[5]

Muzylev N.V., On the uniqueness of simultaneous determination of thermal conductivity and bulk heat capacity, Zh. Vychisl. Mat. Mat. Fiz., 23, pp. 102-108, (1983)

[6]

Shcheglov A.Yu., Inverse problem for a quasilinear heat equation, Vestn. Mosk. Univ., Ser. 15: Vychisl. Mat. Kibern., 2, pp. 8-11, (1987)

[7]

Drozhzhina O.V., A method for numerical recovery of two coefficients in a nonlinear inhomogeneous heat equation, Vestn. Mosk. Univ., Ser. 15: Vychisl. Mat. Kibern., 2, pp. 6-12, (2003)

[8]

Glushkova E.S., Über die eindeutigkeit einiger inverser probleme für die telegraphengleichung, Mathematical Problems in Geophysics, 6, pp. 130-144, (1975)

[9]

Cavaterra C., An inverse problem for a semilinear wave equation, Boll. Univ. Mat. Ital. (B). Ser., 2, pp. 695-711, (1988)

[10]

Qi G.B., Tao W.J., An inverse problem for a one-dimensional semilinear hyperbolic equation with an unknown source, J. Harbin Inst. Tech., 4, pp. 14-20, (1989)

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