Initial boundary value problem for a strongly damped wave equation with a general nonlinearity

TL;DR

This paper establishes a finite time blow-up criterion and lifespan estimates for solutions to a strongly damped semilinear wave equation with general nonlinearity, extending recent results and analyzing effects of different nonlinearities.

Contribution

It introduces a new auxiliary functional and concavity method to analyze blow-up and lifespan for a broad class of nonlinearities in damped wave equations.

Findings

Finite time blow-up criterion established.

Lifespan of solutions estimated from above and below.

Effects of power and logarithmic nonlinearities on blow-up analyzed.

Abstract

In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated from both above and below. This partially extends some results obtained in recent literatures and sheds some light on the similar effect of power type nonlinearity and logarithmic nonlinearity on finite time blow-up of solutions to such problems.