A note on optimal L2-estimates of solutions to some strongly damped σ-evolution equations

Article type: Research Article

Authors: Ikehata, Ryo^{; *}

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

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

Abstract: We consider the Cauchy problem in Rn for the so-called σ-evolution equations with damping terms. We derive asymptotic profiles of solutions with weighted L1,1(Rn) initial data, and investigates the optimality of estimates of solutions in L2-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).

Keywords: σ-evolution equation, damping terms, optimal estimates, weighted L¹-initial data

DOI: 10.3233/ASY-191595

Journal: Asymptotic Analysis, vol. 121, no. 1, pp. 59-74, 2021