Asymptotic profile of solutions for wave equations with frictional and viscoelastic damping terms

Article type: Research Article

Authors: Ikehata, Ryo^{; *} | Sawada, Atsushi

Affiliations: Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan

Correspondence: [*] Corresponding author. E-mail: ikehatar@hiroshima-u.ac.jp.

Abstract: We consider the Cauchy problem in Rn for some types of damped wave equations. We derive asymptotic profiles of solutions with weighted L1,1(Rn) initial data by employing a simple method introduced in [Math. Meth. Appl. Sci. 27 (2004), 865–889].

Keywords: wave equation, frictional term, viscoelastic term, Gauss kernel, asymptotic profiles, Fourier analysis, low frequency, high frequency, weighted L¹-initial data

DOI: 10.3233/ASY-161361

Journal: Asymptotic Analysis, vol. 98, no. 1-2, pp. 59-77, 2016