Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term. (June 2022)

• Record Type: Journal Article
• Authors: Kagei, Yoshiyuki; Takeda, Hiroshi
• Is Part Of: Nonlinear analysis. Volume 219(2022)
• Publication Date: 2022-06
• Subjects: primary 35L72 -- secondary 35B40 35B65; Nonlinear elastic wave equation -- Damping terms -- Consistency -- Smoothing effect -- Asymptotic profile -- The Cauchy problem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112826
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The Cauchy problem for a nonlinear elastic wave equation 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.