Critical Exponents Curve for Semilinear System of Weakly Coupled Effectively Damped Waves with Different Power Nonlinearities
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Authors: A. M. DJAOUTI
DOI: 10.46793/KgJMat2503.375D
Abstract:
In this paper we prove a blow-up result for the semi linear system of weakly coupled effectively damped waves with different power nonlinearities
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where b(t) will be explained in detail in the next sections. We apply the so called “test function method” to determine the range for the exponents p,q > 0 in the nonlinear terms in which local in time existence may not globally prolonged with respect to the t variable under suitable integral sign assumptions for the Cauchy data u0,u1,v0,v1. Since we prove the blow-up in a complementary range for powers of the nonlinear terms to that for the global existence of small data solutions (see [?]), the main blow-up of this paper is optimal.
Keywords:
Weakly coupled hyperbolic systems, damped wave equations, Cauchy problem, blow up, effective dissipation.
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