Applied Mathematics & Information Sciences

Author Country (or Countries)

Kingdom of Saudi Arabia.


In this paper, we study a viscoelastic wave equations of the Kirchhoff type u′′ −f (x) M(k?xuk22 )Dxu− Z t 0 g(t −s)Dxu(s)ds = auln |u|k (1) defined in any spaces dimension. It is well known that from a class of nonlinearities the logarithmic nonlinearity is distinguished by several interesting physical properties. We use weighted spaces to establish the long-time behavior of solution of (1). Furthermore, under convenient hypotheses on g and the initial data, the local-in-time existence of solution is established.

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