GLOBAL EXISTENCE OF SOLUTIONS FOR A WEAKLY COUPLED SYSTEM OF THREE DAMPED ????-EVOLUTION EQUATIONS

GLOBAL EXISTENCE OF SOLUTIONS FOR A WEAKLY COUPLED SYSTEM OF THREE DAMPED ????-EVOLUTION EQUATIONS

A. M. Djaouti

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Abstract

In this paper our purpose is the study of the Cauchy problem for weakly coupled system of three semi-linear damped  -evolution equations. Using pLm XL2 q L2 linear estimates combined with fractional Gagliardo-Nirenberg inequality. We  nd the so-called pp1   p2   p3q planes for the global (in time) existence. Moreover, from the interaction between the parameters m1;m2;m3 P r1; 2q in one hand and  1;  2;  3 ¥ 1 in the other hand. We proved lower bounds for powers nonlinearities similarly to the modi ed Fujita exponent, which are in the form of planes pp1 p2q, pp1 p3q and pp2 p3q.

Keywords

Weakly coupled system;  -evolution equation; frictional damping, visco-elastic damping, Additional regularity; Global existence.