Hadj Kaddour Tayeb, Ali Hakem

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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.


Damped wave equation; weak solution; test function; fractional derivative


Damped wave equation; weak solution; test function; fractional derivative.

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


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