The Cauchy problem for the nonlinear damped wave equation with slowly decaying data
Analysis of PDEs
2019-03-14 v2
Abstract
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the global solution is given by a solution of the corresponding parabolic problem, which shows that the solution of the damped wave equation has the diffusion phenomena. Moreover, we show blow-up of solution and give the estimate of the lifespan for a subcritical nonlinearity. In particular, we determine the critical exponent for any space dimension.
Cite
@article{arxiv.1605.04616,
title = {The Cauchy problem for the nonlinear damped wave equation with slowly decaying data},
author = {Masahiro Ikeda and Takahisa Inui and Yuta Wakasugi},
journal= {arXiv preprint arXiv:1605.04616},
year = {2019}
}
Comments
43 pages. Theorem 1.3 is improved, some errors are corrected and references are updated