Mohammad Shahrouzi - Department of Mathematics, Jahrom University, Jahrom, Iran
Jorge Ferreira - Federal Fluminense University, Department of Exact Sciences, Volta Redonda, RJ, Brazil
Erhan Pişkin - Dicle University, Department of Mathematics, Diyarbakir, Turkey

The present study examined the behavior of solutions for a viscoelastic double-Kirchhoff-type wave equation with nonlocal degenerate damping term and variable exponent nonlinearities. Under appropriate conditions for the data and exponents, we prove the global existence, asymptotic stability, and blow up of solutions with arbitrary initial energy.

global existence, Asymptotic stability, Blow-Up, Kirchhoff-type equation, nonlocal damping, Variable exponent