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Integro-functional equations in the inverse source problem for the wave equation

Integro-functional equations in the inverse source problem for the wave equation ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 9, pp. 1221–1232.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.M. Denisov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 9, pp. 1155–1165. PARTIAL DIFFERENTIAL EQUATIONS Integro-Functional Equations in the Inverse Source Problem for the Wave Equation A. M. Denisov Moscow State University, Moscow, Russia Received March 13, 2006 DOI: 10.1134/S0012266106090011 We prove the existence and uniqueness of solutions of inverse source problems for the wave equation. Two forms of expressions determining the source are considered. The first form is f (u(x, t))p(x), where f (s) is a given function, u(x, t) is the solution of the wave equation, and p(x)is an unknown function. The second form is r(x, t)p(x), where r(x, t) is a given function and p(x) is an unknown function. As additional information for the solution of the inverse problems, the values of the solution of the Cauchy problem for the wave equation are specified on some curve. To prove the existence and uniqueness of solutions, we reduce the inverse problems to integro- functional equations for the unknown function p(x). Inverse source problems for the wave equation were considered in [1–6]. 1. STATEMENT http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Integro-functional equations in the inverse source problem for the wave equation

Denisov, A.
Differential Equations , Volume 42 (9) – Nov 6, 2006
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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106090011
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 9, pp. 1221–1232.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c A.M. Denisov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 9, pp. 1155–1165. PARTIAL DIFFERENTIAL EQUATIONS Integro-Functional Equations in the Inverse Source Problem for the Wave Equation A. M. Denisov Moscow State University, Moscow, Russia Received March 13, 2006 DOI: 10.1134/S0012266106090011 We prove the existence and uniqueness of solutions of inverse source problems for the wave equation. Two forms of expressions determining the source are considered. The first form is f (u(x, t))p(x), where f (s) is a given function, u(x, t) is the solution of the wave equation, and p(x)is an unknown function. The second form is r(x, t)p(x), where r(x, t) is a given function and p(x) is an unknown function. As additional information for the solution of the inverse problems, the values of the solution of the Cauchy problem for the wave equation are specified on some curve. To prove the existence and uniqueness of solutions, we reduce the inverse problems to integro- functional equations for the unknown function p(x). Inverse source problems for the wave equation were considered in [1–6]. 1. STATEMENT

Journal

Differential Equations – Springer Journals

Published: Nov 6, 2006

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