Nonexistence of global solutions to system of semi-linear fractional evolution equations

Authors : Medjahed Djilali, Ali Hakem

Pages : 171-177

Doi:10.32323/ujma.396407

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Publication Date : 2018-09-30

Article Type : Research

Abstract :In this research we are interested to Cauchy problem for system of semi-linear fractional evolution equations. Some authors were concerned with studying of global existence of solutions for the hyperbolic nonlinear equations with a damping term. Our goal is to extend some results obtained by the authors, by studying the system of semi-linear hyperbolic equations with fractional damping term and fractional Laplacian .Thanks to the test functions method, we prove the nonexistence of nontrivial global weak solutions to the problem. 
Keywords : Derivatives in the sense of Caputo, Fractional Laplacian, Fujita's critical exponent, Test function, Weak solution