Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation

In this paper, a class of nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo–Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given.

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