Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms

Article type: Research Article

Authors: Ikehata, Ryo^a | Michihisa, Hironori^{b; *}

Affiliations: [a] Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan. E-mail: ikehatar@hiroshima-u.ac.jp | [b] Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan. E-mail: hi.michihisa@gmail.com

Correspondence: [*] Corresponding author. E-mail: hi.michihisa@gmail.com.

Abstract: In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and those of heat equations can be seen by comparing the second order expansions of them. In order to analyze such effects we consider the weighted L1 initial data. We also give some lower bounds which show the optimality of obtained expansions.

Keywords: Wave equation, moment condition, asymptotic expansion, lower bounds estimates, diffusion phenomena, double damping terms

DOI: 10.3233/ASY-181516

Journal: Asymptotic Analysis, vol. 114, no. 1-2, pp. 19-36, 2019