General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

TL;DR

This paper investigates the conditions under which solutions to a nonlinear wave equation with memory and fractional boundary damping either decay globally or blow up, using Lyapunov functionals and energy methods.

Contribution

It introduces a new analysis framework for nonlinear wave equations with fractional boundary damping and memory, establishing criteria for decay and blow-up of solutions.

Findings

Solutions decay globally under certain conditions.

Solutions blow up with nonpositive initial energy.

Lyapunov functional method effectively analyzes decay and blow-up.

Abstract

The paper studies the global existence and general decay of solutions using Lyaponov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow up of solutions with nonpositive initial energy.