NONEXISTENCE RESULTS FOR SEMI-LINEAR MOORE-GIBSON-THOMPSON EQUATION WITH NON LOCAL OPERATOR
نویسندگان
چکیده
We study the nonexistence of global weak solutions to following semi-linear Moore - Gibson-Thompson equation with nonlinearity derivative type, namely,$$\left\{\begin{array}{l}u_{ttt}+u_{tt}-\Delta u-(-\Delta )^{\frac{\alpha}{2}}u_{t}=|u_t|^p,\quad x\in \R^n,\quad t>0,\\u(0,x)= u_0(x),\quad u_t(0,x)=u_1(x), \quad u_{tt}(0,x)= u_2(x) \R^n,\end{array}\right.$$where $\alpha\in (0, 2],\quad p> 1,$ and $(-\Delta)^{\frac{\alpha}{2}}$ is fractional Laplacian operator order $\frac{\alpha}{2}$. Then, this result extended case a weakly coupledsystem. intend apply method modified test function establish results overcome some difficulties as well caused by well-known $(-\Delta)^{\frac{\alpha}{2}}$.The obtained in paper extend several contributions field.
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ژورنال
عنوان ژورنال: Advances in the theory of nonlinear analysis and its applications
سال: 2022
ISSN: ['2587-2648']
DOI: https://doi.org/10.31197/atnaa.947937