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

Kazunori Goto; Fumihiko Hirosawa

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arXiv · 2409.19889

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

Kazunori Goto·Fumihiko Hirosawa

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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.

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Kazunori Goto, Fumihiko Hirosawa. 2024-09-30. On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data. https://arxiv.org/abs/2409.19889

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