Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms

Abstract

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.

Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term

“…In addition, they gave some estimates for lower bound of the blow up time. On the other hand, the other some studies with degenerate damping terms are see (see [21][22][23][24][25][26][27][28][29]).…”

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

“…where is a di¤erentiable nonincreasing positive function, see [10], [17], [31]. Recently, the condition (1.10) have been relaxed by Mesloub and Boulaaras [27], Boumaza and Boulaaras [2], Conti and Pata [5], in which the kernel g haven't been necessarily decreasing.…”