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arXiv · 2109.04618

Smoothing effect and asymptotic behavior of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of $L^{p}$-Sobolev spaces

Yoshiyuki Kagei·Hiroshi Takeda
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Abstract

The Cauchy problem for nonlinear elastic wave equations with viscoelastic damping terms is investigated in $L^{p}$ framework. It is proved that the small global solutions constructed in $L^{2}$-Sobolev spaces in our preceding paper [12] satisfies consistency property corresponding to the additional regularity of the initial data. As a result, sharp estimates in $t$ and approximation formulas by the diffusion waves are established.

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Yoshiyuki Kagei, Hiroshi Takeda. 2021-09-10. Smoothing effect and asymptotic behavior of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of $L^{p}$-Sobolev spaces. https://arxiv.org/abs/2109.04618

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