NONEXISTENCE RESULTS FOR SEMI-LINEAR MOORE-GIBSON-THOMPSON EQUATION WITH NON LOCAL OPERATOR

Authors : Hakem ALI, Svetlin GEORGİEV

Pages : 191-201

Doi:10.31197/atnaa.947937

View : 33 | Download : 5

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :We study the nonexistence of global weak solutions to the following semi-linear Moore - Gibson- Thompson equation with the nonlinearity of derivative type, namely, $$ \left\{ \begin{array}{l} u_{ttt}+u_{tt}-\Delta u-insert ignore into journalissuearticles values(-\Delta );^{\frac{\alpha}{2}}u_{t} =|u_t|^p,\quad x\in \R^n,\quad t>0,\\ uinsert ignore into journalissuearticles values(0,x);= u_0insert ignore into journalissuearticles values(x);,\quad u_tinsert ignore into journalissuearticles values(0,x);=u_1insert ignore into journalissuearticles values(x);, \quad u_{tt}insert ignore into journalissuearticles values(0,x);= u_2insert ignore into journalissuearticles values(x); \quad x\in \R^n, \end{array} \right. $$ where $\alpha\in insert ignore into journalissuearticles values(0, 2],\quad p> 1,$ and $insert ignore into journalissuearticles values(-\Delta);^{\frac{\alpha}{2}}$ is the fractional Laplacian operator of order $\frac{\alpha}{2}$. Then, this result is extended to the case of a weakly coupled system. We intend to apply the method of a modified test function to establish nonexistence results and to overcome some difficulties as well caused by the well-known fractional Laplacian $insert ignore into journalissuearticles values(-\Delta);^{\frac{\alpha}{2}}$.The results obtained in this paper extend several contributions in this field.
Keywords : Test functions, nonexistence, lifespan estimates

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