The problem of determining source term in a semilinear wave equation is considered. The source term is represented as the product ƒ(u(x, t))p(x), where ƒ(s) is a given function, u(x, t) is a solution to Cauchy problem for wave equation, p(x) is an unknown function. To determine p(x) the additional information on the solution of the Cauchy problem u(α(t), t) = g(t), u(β(t), t) = h(t) is used. Theorems of existence and uniqueness of solution to an inverse problem in the class of continuous functions p(x) and in the class of functions p(x) = p o + xq(x), where q(x) is continuous, are proved.

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Existence and uniqueness of solution to the problem of determining source term in a semilinear wave equation
A. M. Denisov∗
∗Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia. E-mail: den@cs.msu.su
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 8, Pages 767–784, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406779768346,
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