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arXiv · 2407.17179

On $L^p-L^{p'}$ estimates for a class of strongly damped wave equations

Haidar Mohamad
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Abstract

The purpose of this paper is to obtain a fundamental $L^p-L^{p'}$ estimate for a class of a strongly damped wave equations where the damping operator is given by $-\delta \Delta$ with $\delta \geq 0$ and the constant in the estimate is independent of the damping parameter $\delta.$ The method used here is based on an estimate of the semigroup associated to the linear equation on the Besov spaces and their elementary properties.

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Haidar Mohamad. 2024-07-24. On $L^p-L^{p'}$ estimates for a class of strongly damped wave equations. https://arxiv.org/abs/2407.17179

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