Asymptotic behaviors of global solutions for a semilinear diffusion equation in the de Sitter spacetime

Article type: Research Article

Authors: Nakamura, Makoto^{a; *} | Takeda, Hiroshi^b

Affiliations: [a] Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560, Japan. E-mail: [email protected] | [b] Department of Intelligent Mechanical Engineering, Faculty of Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi, Higashi-ku, Fukuoka 811-0295, Japan. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: A semilinear diffusion equation is considered in the de Sitter spacetime with the spatially flat curvature. Global solutions for small initial data and their asymptotic behaviors in high order are obtained. Some effects of the spatial expansion and contraction are studied through the problem.

Keywords: Semilinear diffusion equation, global solution, asymptotic behavior, de Sitter spacetime

DOI: 10.3233/ASY-201652

Journal: Asymptotic Analysis, vol. 125, no. 3-4, pp. 203-245, 2021