Revista de la
Unión Matemática Argentina
Blow-up of positive-initial-energy solutions for nonlinearly damped semilinear wave equations
Mohamed Amine Kerker
Volume 63, no. 2 (2022), pp. 293–303

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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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