Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms

TL;DR

This paper investigates the conditions under which solutions to a nonlinear wave equation with damping terms exist globally or blow up in finite time, depending on the nonlinearity's growth rate.

Contribution

It establishes a threshold criterion for global existence versus blow-up for nonlinear wave equations with combined damping effects.

Findings

Identifies critical exponent separating global existence and blow-up regimes.

Provides a classification based on the growth order of the nonlinearity.

Analyzes the influence of damping terms on solution behavior.

Abstract

In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. Our aim is to obtain the threshold, to classify the global existence of solution for small data or the finite time blow-up pf the solution, with respect to the growth order of the nonlinearity.