General Decay and Blow-up Results of a Robin-Dirichlet Problem for a Pseudoparabolic Nonlinear Equation of Kirchhoff-Carrier Type with Viscoelastic Term

Abstract

In this paper, we investigate the Robin-Dirichlet problem for a nonlinear pseudoparabolic equation of Kirchhoff-Carrier type with viscoelastic term. Under suitable assumptions on the initial data and the relaxation function included in the viscoelastic term, we obtain sufficient conditions for the existence, uniqueness, blow-up, and decay of a weak solution. The results obtained here extend the ones in a previous paper of the authors (Ngoc et al., Math. Meth. Appl. Sci. 44(11), 8697–8725, 26).