Finite time blow-up for quasilinear wave equations with nonlinear dissipation
DOI:
https://doi.org/10.24193/subbmath.2022.4.09Keywords:
Nonlinear wave equation, strong damping, blow-upAbstract
In this paper we consider a class of quasilinear wave equations \[u_{tt}-\Delta_{\alpha} u-\omega_1\Delta u_t-\omega_2\Delta_{\beta}u_t+\mu\vert u_t\vert^{m-2}u_t=\vert u\vert^{p-2}u,\]associated with initial and Dirichlet boundary conditions. Under certain conditions on \(\alpha,\beta,m,p\), we show that any solution with positive initial energy, blows up in finite time. Furthermore, a lower bound for the blow-up time will be given.Downloads
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2022-12-01
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