Vanishing, moving and immovable interfaces in fast reaction limits
Vanishing, moving and immovable interfaces in fast reaction limits
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快速反应极限内的消失、移动和不动界面
DOI：
10.1016/j.jde.2017.04.009
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发表时间：
2017
影响因子：
2.4
通讯作者：
H. Murakawa and H. Ninomiya
中科院分区：
文献类型：
--
作者：
M. Iida;H. Monobe;H. Murakawa and H. Ninomiya
我们考虑了一类称为快速反应极限的奇异极限问题。快速反应极限问题涉及研究反应扩散系统在反应速度很快时的解的行为。近几十年来，人们对双组分体系的快速反应极限进行了研究。在大多数这样的系统中，每个组分的快速反应项由相同的函数表示。具有不同快反应项的体系的快反应极限仍远未得到很好的理解。本文主要研究反应项由各种幂的单项函数组成的反应扩散系统。研究了该体系在快速反应极限下的界面行为。根据功率的不同，观察到三种类型的行为：(I)初始界面瞬间消失，(Ii)界面以有限速度传播，(Iii)界面不移动。
We consider a type of singular limit problem called thefast 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.