Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term

2021/09/10 by Kagei, Yoshiyuki, Takeda, Hiroshi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.04628

Abstract

The Cauchy problem for a nonlinear elastic wave equations with viscoelastic damping terms is considered on the 3 dimensional whole space. Decay and smoothing properties of the solutions are investigated when the initial data are sufficiently small; and asymptotic profiles as t → ∞ are also derived.

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