Vanishing, moving and immovable interfaces in fast reaction limits

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Iida, M.¹  Monobe, H.²  Murakawa, H.³  Ninomiya, H.⁴ 

[1] Univ Miyazaki, Ctr Sci & Engn Educ, Miyazaki 8892192, Japan

[2] Okayama Univ, Res Inst Interdisciplinary Sci, Kita Ku, 3-1-1 Tsushima Naka, Okayama 7008530, Japan

[3] Kyushu Univ, Fac Math, Nishi Ku, 744 Motooka, Fukuoka 8190395, Japan

[4] Meiji Univ, Sch Interdisciplinary Math Sci, Nakano Ku, 4-21-1 Nakano, Tokyo 1648525, Japan

关键词: Free boundary problem;    Singular limit problem;    Fast reaction limit;    Reaction-diffusion system;   

DOI  :  10.1016/j.jde.2017.04.009

来源: Elsevier

【 摘 要 】

We consider a type of singular limit problem called the fast reaction limit. The problem of the fast reaction limit involves studying the behaviour of solutions of reaction diffusion systems when the reaction speeds are very fast. Fast reaction limits of two-component systems have been studied in recent decades. In most of these systems, the fast reaction terms of each component are represented by the same function. Fast reaction limits of systems with different fast reaction terms are still far from being well understood. In this paper, we focus on a reaction diffusion system for which the reaction terms consist of monomial functions of various powers. The behaviour of interfaces arising in the fast reaction limit of this system is studied. Depending on the powers, three types of behaviour are observed: (i) the initial interface vanishes instantaneously, (ii) the interface propagates at a finite speed, and (iii) the interface does not move. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free