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

2021/09/10 by Yoshiyuki Kagei, Kagei, Yoshiyuki, Hiroshi Takeda +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2109.04618

openalex publication_date 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²-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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