This article is cited in 9 papers

Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination

A. Yu. Shcheglov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: The inverse problem of recovering a solution-dependent coefficient multiplying the lowest derivative in a hyperbolic equation is investigated. As overdetermination is required in the inverse problem, an additional condition is imposed on the solution to the equation with a fixed value of the timelike variable. Global uniqueness and local existence theorems are proved for the solution to the inverse problem. An iterative method is proposed for solving the inverse problem.

Key words: quasi-linear hyperbolic equations, inverse coefficient problem, iterative method, numerical solution.

UDC: 519.633.9

Received: 24.12.2003
Revised: 10.11.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:4, 616–635

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