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Existence and uniqueness of solution to the problem of determining source term in a semilinear wave equation
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A. M. Denisov
Published/Copyright:
2006
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) = po + xq(x), where q(x) is continuous, are proved.
Published Online: --
Published in Print: 2006-12-01
Copyright 2006, Walter de Gruyter
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- Dynamical inverse problem for a Lamé type system
- Existence and uniqueness of solution to the problem of determining source term in a semilinear wave equation
- Conformal mapping and an inverse impedance boundary value problem
- Conditional stability stopping rule for gradient methods applied to inverse and ill-posed problems
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Articles in the same Issue
- Dynamical inverse problem for a Lamé type system
- Existence and uniqueness of solution to the problem of determining source term in a semilinear wave equation
- Conformal mapping and an inverse impedance boundary value problem
- Conditional stability stopping rule for gradient methods applied to inverse and ill-posed problems
- Some tendencies in the Tikhonov regularization of ill-posed problems
