Initial boundary value problem for a strongly damped wave equation with a general nonlinearity
Analysis of PDEs
2020-10-22 v1
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.
Keywords
Cite
@article{arxiv.2010.10696,
title = {Initial boundary value problem for a strongly damped wave equation with a general nonlinearity},
author = {Hui Yang and Yuzhu Han},
journal= {arXiv preprint arXiv:2010.10696},
year = {2020}
}