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Inverse problem for a quasilinear wave equation

Inverse problem for a quasilinear wave equation ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 8, pp. 1123–1131.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.M. Denisov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 8, pp. 1097–1105. PARTIAL DIFFERENTIAL EQUATIONS A. M. Denisov Moscow State University, Moscow, Russia Received April 5, 2007 DOI: 10.1134/S0012266107080101 The present paper deals with the proof of the existence and uniqueness of a solution of an inverse problem for a quasilinear wave equation with an unknown coefficient q(x) multiplying a lower-order derivative. The values of the solution of the Cauchy problem for this equation on some curve serve as additional information for the solution of the inverse problem. The proof of the existence and uniqueness of the solution of the inverse problem is based on the reduction of the problem to an integro-functional equation for the unknown function q(x). A similar approach was used in [1, 2] for the analysis of the inverse problem of finding an unknown function occurring in the nonlinear term specifying the source in the wave equation. Inverse problems for the wave equation were considered in a number of papers (e.g., see [3–7]). 1. STATEMENT OF THE PROBLEM AND THE MAIN http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Inverse problem for a quasilinear wave equation

Denisov, A.
Differential Equations , Volume 43 (8) – Oct 26, 2007
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266107080101
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 8, pp. 1123–1131.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.M. Denisov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 8, pp. 1097–1105. PARTIAL DIFFERENTIAL EQUATIONS A. M. Denisov Moscow State University, Moscow, Russia Received April 5, 2007 DOI: 10.1134/S0012266107080101 The present paper deals with the proof of the existence and uniqueness of a solution of an inverse problem for a quasilinear wave equation with an unknown coefficient q(x) multiplying a lower-order derivative. The values of the solution of the Cauchy problem for this equation on some curve serve as additional information for the solution of the inverse problem. The proof of the existence and uniqueness of the solution of the inverse problem is based on the reduction of the problem to an integro-functional equation for the unknown function q(x). A similar approach was used in [1, 2] for the analysis of the inverse problem of finding an unknown function occurring in the nonlinear term specifying the source in the wave equation. Inverse problems for the wave equation were considered in a number of papers (e.g., see [3–7]). 1. STATEMENT OF THE PROBLEM AND THE MAIN

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Differential Equations – Springer Journals

Published: Oct 26, 2007

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