Geodesic
Results of nonexistence of solutions for some nonlinear evolution problems
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 269-284.

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In the present paper, we prove nonexistence results for the following nonlinear evolution equation, see works of T. Cazenave and A. Haraux (1990) and S. Zheng (2004), $$ u_{tt} +f(x)u_t +(-\Delta)^{\alpha/2}(u^m)= h(t,x) |u|^{p}, $$ posed in $(0,T)\times \mathbb{R}^{N},$ where $(-\Delta)^{{\alpha}/{2}}, 0\alpha \leq 2$ is ${\alpha}/{2}$-fractional power of $\,-\Delta.$ Our method of proof is based on suitable choices of the test functions in the weak formulation of the sought solutions. Then, we extend this result to the case of a $2\times2$ system of the same type.
DOI : 10.14712/1213-7243.2019.001
Classification : 35A01, 35D30, 47J35
Keywords: nonexistence; test functions; global weak solution; fractional Laplacian; critical exponent 
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Djilali, Medjahed; Hakem, Ali. Results of nonexistence of solutions for some nonlinear evolution problems. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 269-284. doi : 10.14712/1213-7243.2019.001. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2019.001/

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