Study of semi-linear $\sigma$-evolution equations with frictional and visco-elastic damping

Hironori Michihisa; Tuan Anh Dao

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arXiv · 1906.04471

Study of semi-linear $\sigma$-evolution equations with frictional and visco-elastic damping

Hironori Michihisa·Tuan Anh Dao

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Abstract

In this article, we study semi-linear $\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\sigma\ge 1$. We are interested in investigating not only higher order asymptotic expansions of solutions but also diffusion phenomenon in the $L^p-L^q$ framework, with $1\le p\le q\le \infty$, to the corresponding linear equations. By assuming additional $L^{m}$ regularity on the initial data, with $m\in [1,2)$, we prove the global (in time) existence of small data energy solutions and indicate the large time behavior of the global obtained solutions as well to semi-linear equations. Moreover, we also determine the so-called critical exponent when $\sigma$ is integers.

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Hironori Michihisa, Tuan Anh Dao. 2019-06-11. Study of semi-linear $\sigma$-evolution equations with frictional and visco-elastic damping. https://arxiv.org/abs/1906.04471

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