A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains

Lingyang Liu

A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains

Analysis of PDEs 2021-03-23 v2

Authors: Lingyang Liu

Abstract

In this paper, we study the large time behavior of a class of wave equation with a nonlinear dissipation in non-cylindrical domains. The result we obtained here relaxes the conditions for the nonlinear term coefficients (in precise, that is $\beta(t)|u|^\rho u$ ) in \cite{alb} and \cite{ha} (which require $\beta(t)$ to be a constant or $\beta(t)$ to be decreasing with time $t$ ) and has less restriction for the defined regions.

Keywords

nonlinear wave equations energy decay for wave equations parabolic equations

Cite

@article{arxiv.2103.09678,
  title  = {A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains},
  author = {Lingyang Liu},
  journal= {arXiv preprint arXiv:2103.09678},
  year   = {2021}
}

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