自催化
静止状态
反应扩散系统
扩散
饱和(图论)
同种类的
常量(计算机编程)
统计物理学
图案形成
数学
反应速率常数
达克勒数
Neumann边界条件
热力学
边值问题
数学分析
化学
经典力学
物理化学
物理
动力学
燃烧
计算机科学
量子力学
遗传学
组合数学
程序设计语言
生物
作者
Rui Peng,Junping Shi,Mingxin Wang
出处
期刊:Nonlinearity
[IOP Publishing]
日期:2008-05-21
卷期号:21 (7): 1471-1488
被引量:97
标识
DOI:10.1088/0951-7715/21/7/006
摘要
Understanding of spatial and temporal behaviour of interacting species or reactants in ecological or chemical systems has become a central issue, and rigorously determining the formation of patterns in models from various mechanisms is of particular interest to applied mathematicians. In this paper, we study a bimolecular autocatalytic reaction–diffusion model with saturation law and are mainly concerned with the corresponding steady-state problem subject to the homogeneous Neumann boundary condition. In particular, we derive some results for the existence and non-existence of non-constant stationary solutions when the diffusion rate of a certain reactant is large or small. The existence of non-constant stationary solutions implies the possibility of pattern formation in this system. Our theoretical analysis shows that the diffusion rate of this reactant and the size of the reactor play decisive roles in leading to the formation of stationary patterns.
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