On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data
Analysis of PDEs
2024-10-01 v1
Abstract
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For such a problem, which have been difficult to deal with in previous research, we prove energy decay estimates by introducing a new condition for the coefficients to evaluate oscillating cancellation of the energy, and smooth initial data such as in the Gevrey class.
Keywords
Cite
@article{arxiv.2409.19889,
title = {On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data},
author = {Kazunori Goto and Fumihiko Hirosawa},
journal= {arXiv preprint arXiv:2409.19889},
year = {2024}
}