Asian Journal of Mathematics and Computer Research

ASYMPTOTIC STABILITY FOR A WAVE EQUATION WITH SPACE-TIME DEPENDENT ON DAMPING TERM AND INFINITE MEMORY

FERHAT MOHAMED

Department of Mathematics, USTO University, 31000 Oran, Algeria.

HAKEM ALI *

Laboratory ACEDP, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we consider a wave equation with space-time dependent on damping term and infinite memory. Based on the weighted energy method, we obtain L²- decay rates of the solutions. This work is motivated by a recent one of [1] with necessary modification imposed by the nature of our problem.

Keywords: Space-time, infinite memory, weighted energy method

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