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A. M. Denisov

Existence and uniqueness of solution to the problem of determining source term in a semilinear wave equation

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.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 14, 12/2006
Pages: 767 - 784

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