Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source
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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.
CitationZhang, X., Chai, S., & Wu, J. (2017). Blow-up of solutions to a coupled quasilinear viscoelastic wave system with nonlinear damping and source. Electronic Journal of Differential Equations, 2017(78), pp. 1-11.
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