On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data

Fuente: arXiv
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Autori principali: Goto, Kazunori, Hirosawa, Fumihiko
Natura: Preprint
Pubblicazione: 2024
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author Goto, Kazunori
Hirosawa, Fumihiko
author_facet Goto, Kazunori
Hirosawa, Fumihiko
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_19889
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data
Goto, Kazunori
Hirosawa, Fumihiko
Analysis of PDEs
35L05 (Primary) 35L15 (Secondary)
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.
title On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data
topic Analysis of PDEs
35L05 (Primary) 35L15 (Secondary)
url https://arxiv.org/abs/2409.19889