A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

Wenhui Chen; Alessandro Palmieri

doi:10.3934/eect.2020085

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2021, Volume 10, Issue 4: 673-687. Doi: 10.3934/eect.2020085

This issue Previous Article Next Article Solvability in abstract evolution equations with countable time delays in Banach spaces: Global Lipschitz perturbation

A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

Wenhui Chen^1, , and
Alessandro Palmieri^2,

1.
Institute of Applied Analysis, Faculty of Mathematics and Computer Science, Technical University Bergakademie Freiberg, 09596, Germany
2.
Department of Mathematics, University of Pisa, 56127, Italy

^* Corresponding author: Wenhui Chen
^* Corresponding author: Wenhui Chen

Received: December 31, 2019

Revised: May 31, 2020

Early access: August 2020

Published: December 2021

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Abstract

In this paper, we study the blow – up of solutions to the semilinear Moore – Gibson – Thompson (MGT) equation with nonlinearity of derivative type $ |u_t|^p $ in the conservative case. We apply an iteration method in order to study both the subcritical case and the critical case. Hence, we obtain a blow – up result for the semilinear MGT equation (under suitable assumptions for initial data) when the exponent $ p $ for the nonlinear term satisfies $ 1<p\leqslant (n+1)/(n-1) $ for $ n\geqslant2 $ and $ p>1 $ for $ n = 1 $. In particular, we find the same blow – up range for $ p $ as in the corresponding semilinear wave equation with nonlinearity of derivative type.

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Mathematics Subject Classification: Primary: 35B44, 35L30; Secondary: 35L76, 35B33, 35L25.

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