Contraction-Galerkin method for a semi-linear wave equation

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January 2010, 9(1): 141-160. doi: 10.3934/cpaa.2010.9.141

Contraction-Galerkin method for a semi-linear wave equation

1.	Department of Mathematical Sciences, P.O. Box 3000, FIN-90014 University of Oulu, Finland

Received January 2009 Revised August 2009 Published October 2009

Abstract
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In this paper we consider the unique solvability of initial-boundary value problems of semi-linear wave equations with space-time dependent coefficients and special mixed non-homogeneous boundary values which form the so-called boundary-like antiperiodic condition. The procedure in this paper is the combination of the Galerkin method and a contraction.

Keywords: semi-linear wave equation, Antiperiodic, contraction, solvability, Galerkin method, mixed non-homogenenous boundary values, initial-boundary value problem, uniqueness..

Mathematics Subject Classification: Primary: 35L15, 35L70; Secondary: 35A0.

Citation: Út V. Lê. Contraction-Galerkin method for a semi-linear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 141-160. doi: 10.3934/cpaa.2010.9.141

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