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• W3033972371 abstract "In this work, the Cauchy problem for the semilinear Moore-Gibson-Thompson (MGT) equation with power nonlinearity $|u|^p$ on the right-hand side is studied. Applying $L^2-L^2$ estimates and a fixed point theorem, we obtain local (in time) existence of solutions to the semilinear MGT equation. Then, the blow-up of local in time solutions is proved by using an iteration method, under certain sign assumption for initial data, and providing that the exponent of the power of the nonlinearity fulfills $1 < p leqslant p_{mathrm{Str}}(n)$ for $n geqslant2$ and $p>1$ for $n=1$. Here the Strauss exponent $p_{mathrm{Str}}(n)$ is the critical exponent for the semilinear wave equation with power nonlinearity. In particular, in the limit case $p=p_{mathrm{Str}}(n)$ a different approach with a weighted space average of a local in time solution is considered." @default.
• W3033972371 created "2020-06-12" @default.
• W3033972371 creator A5020272049 @default.
• W3033972371 creator A5083823085 @default.
• W3033972371 date "2020-01-01" @default.
• W3033972371 modified "2023-10-15" @default.
• W3033972371 title "Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case" @default.
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• W3033972371 doi "https://doi.org/10.3934/dcds.2020236" @default.
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