### LOCAL EXISTENCE AND SUFFICIENT CONDITIONS OF THE NON-GLOBAL SOLUTION FOR WEIGHTED DAMPED WAVE EQUATIONS

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#### Abstract

In this paper we study the following Cauchy problem of the weighted

damped wave equation with nonlinear memory

in the multi-dimensional real space Rn. where, m > 1, p > 1, 0 < gama < 1 and Delta is the usual Laplace operator and g is a positive smooth function which will be specified later. Firstly, we will prove the existence and uniqueness of the local solution theorem and, secondly, the nonexistence of the global solutions theorem is established.

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DOI: https://doi.org/10.22190/FUMI1705629T

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