Abstract
This article is concerned with the decay and blow-up properties of a nonlinear viscoelastic wave equation with strong damping. We first show a local existence theorem. Then, we prove the global existence of solutions and establish a general decay rate estimate. Finally, we show the finite time blow-up result for some solutions with negative initial energy and positive initial energy.
Highlights
1 Introduction In this work we investigate the decay and blow-up properties of the nonlinear viscoelastic wave equation of the form:
In this paper, we study a nonlinear viscoelastic wave equation with strong damping
We prove the global existence of solutions and establish a general decay rate estimate
Summary
In this work we investigate the decay and blow-up properties of the nonlinear viscoelastic wave equation of the form:. Guesmia et al [8] combined Li and He Boundary Value Problems (2018) 2018:153 the techniques given in [17] with the character of Kirchhoff equation and obtained the optimal decay rate estimate of solution energy. For the case of wave equation with nonlinear boundary damping and source terms, Vitillaro [21] established the local and global existence of solutions under reasonable conditions on the initial data. Song [19] proved the finite time blow-up of solutions whose initial data have arbitrarily high initial energy It is worth mentioning some other literatures concerning existence and nonexistence of wave equation, namely [7, 9, 11, 13, 14, 20] and the references therein.
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