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

Hadj Kaddour Tayeb, Ali Hakem

DOI Number
10.22190/FUMI1705629T
First page
629
Last page
657

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.


Keywords

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

Keywords


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

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

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