A note on optimal L 2 -estimates of solutions to some strongly damped σ-evolution equations-Reference-Cited by-同舟云学术

A note on optimal L 2 -estimates of solutions to some strongly damped σ-evolution equations

Published:2020-12-02 Issue:1 Volume:121 Page:59-74
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Ikehata Ryo¹

Affiliation:

1. Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan. E-mail: ikehatar@hiroshima-u.ac.jp

Abstract

We consider the Cauchy problem in R n for the so-called σ-evolution equations with damping terms. We derive asymptotic profiles of solutions with weighted L 1 , 1 ( R n ) initial data, and investigates the optimality of estimates of solutions in L 2 -sense. The obtained results will generalize and compensate those already known in (J. Math. Anal. Appl. 478 (2019) 476–498, J. Diff. Eqns 257 (2014) 2159–2177, Diff. Int. Eqns 30 (2017), 505–520).

Publisher

IOS Press

Subject

General Mathematics

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