Diffusion phenomenon for abstract linear wave equations with time decaying coefficients of propagation and dissipation

Article type: Research Article

Authors: Yamazaki, Taeko^{; *}

Affiliations: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan. E-mail: yamazaki@ma.noda.tus.ac.jp; Tel.: 04-7122-9321; Fax: 04-7123-9762

Correspondence: [*] Corresponding author. E-mail: yamazaki@ma.noda.tus.ac.jp.

Abstract: We show diffusion phenomenon for linear abstract dissipative wave equations with time dependant coefficients of propagation speed and dissipation. Coefficients are decaying in time but not assumed to be monotone.

Keywords: Diffusion phenomenon, abstract linear dissipative wave equation, time dependent propagation speed, time dependent dissipation

DOI: 10.3233/ASY-201665

Journal: Asymptotic Analysis, vol. 124, no. 1-2, pp. 109-161, 2021