On the wave equation with variable exponent nonlinearity and distributive delay

TL;DR

This paper investigates a nonlinear wave equation with variable exponents and a distributive delay, establishing conditions for global existence, nonexistence, and decay rates of solutions.

Contribution

It introduces a novel analysis of wave equations with variable exponent nonlinearities and distributive delays, providing new results on solution behavior.

Findings

Global nonexistence time can be bounded.

Global existence is proven under certain initial data conditions.

Decay rates of solutions are established.

Abstract

In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be dominated. Secondly, global existence of solutions is shown under some suitable conditions on the initial data. Finally, the decay rates of that solutions are established as well.