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Existence and uniqueness of an inverse problem for nonlinear Klein-Gordon equation. (English) Zbl 1418.35384

Summary: In this paper, an initial boundary value problem for nonlinear Klein-Gordon equation is considered. Giving an additional condition, a time-dependent coefficient multiplying nonlinear term is determined, and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem.

MSC:

35R30 Inverse problems for PDEs
35L70 Second-order nonlinear hyperbolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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