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-up.Abstract
In this paper we consider a class of quasilinear wave equations utt − ∆αu − ω1∆ut − ω2∆βut + µ|ut|m−2ut = |u|p−2u, associated with initial and Dirichlet boundary conditions. Under certain conditions on α, β, 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.
Mathematics Subject Classification (2010): 35B44, 35L05, 35L20, 35L72.
Received 02 March 2020; Accepted 13 April 2020.
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