Blow-up of Solutions to a Coupled Quasilinear Viscoelastic Wave System with Nonlinear Damping and Source
نویسندگان
چکیده
We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-increasing functions and the initial energy is negative. The competition relations among the nonlinear principal parts are not constant functions, the viscoelasticity terms, dampings and sources are analyzed by using perturbed energy method. The blow-up result is proved under some conditions on the nonlinear principal parts, viscoelasticity terms, dampings and sources by a contradiction argument.
منابع مشابه
Blow-up of arbitrarily positive initial energy solutions for a viscoelastic wave system with nonlinear damping and source terms
*Correspondence: [email protected] School of Mathematical Sciences, Ocean University of China, Qingdao, P.R. China Abstract This work is concerned with the Dirichlet initial boundary problem for a semilinear viscoelastic wave system with nonlinear weak damping and source terms. For nonincreasing positive functions g and h, we show the finite time blow-up of some solutions whose initial data hav...
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