Blow-up of positive initial energy solutions for nonlinearly damped semilinear wave equations

Authors

  • Mohamed Amine Kerker Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria

DOI:

https://doi.org/10.33044/revuma.2099

Abstract

We consider a class of semilinear wave equations with both strongly and nonlinear weakly damped terms,
\[
u_{tt}-\Delta u-\omega\Delta u_t+\mu\vert u_t\vert^{m-2}u_t=\vert u\vert^{p-2}u,
\]
associated with initial and Dirichlet boundary conditions. Under certain conditions, we show that any solution with arbitrarily high positive initial energy blows up in finite time if $m < p$. Furthermore, we obtain a lower bound for the blow-up time.

 

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Published

2022-08-03