A semilinear wave equation with space-time dependent coefficients and a memory boundarylike antiperiodic condition: Regularity and stability

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3494574· OSTI ID:21476579

Le, Ut V ^[1]

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

This paper deals with regularity and stability of solutions to an initial-boundary value problem of a semilinear wave equation. This equation admits space-time dependent coefficients and a memory boundarylike antiperiodic condition. For regularity or existence of a unique strong solution, the Faedo-Galerkin method and the energy method, associated with the maximal solution of a nonlinear Volterra integral equation, are applied. Then, as an application of the regularity result, stability of this unique strong solution is obtained by the energy method.

• OSTI ID: 21476579
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 10; Other Information: DOI: 10.1063/1.3494574; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
SPACE-TIME
STABILITY
VOLTERRA INTEGRAL EQUATIONS
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
INTEGRAL EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS