Communications on Pure and Applied Analysis (CPAA)

Contraction-Galerkin method for a semi-linear wave equation

Pages: 141 - 160, Volume 9, Issue 1, January 2010      doi:10.3934/cpaa.2010.9.141

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Út V. Lê - Department of Mathematical Sciences, P.O. Box 3000, FIN-90014 University of Oulu, Finland (email)

Abstract: 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:  Antiperiodic, contraction, Galerkin method, initial-boundary value problem, semi-linear wave equation, mixed non-homogenenous boundary values, solvability, uniqueness.
Mathematics Subject Classification:  Primary: 35L15, 35L70; Secondary: 35A05.

Received: January 2009;      Revised: August 2009;      Available Online: October 2009.