Bistable Reaction‐Diffusion Equations and Excitable Media
Bistable Reaction‐Diffusion Equations and Excitable Media
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双稳态反应扩散方程和可激发介质
DOI：
10.1002/mana.19831120107
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发表时间：
1983
影响因子：
1
通讯作者：
J. Gärtner
中科院分区：
文献类型：
--
作者：
J. Gärtner
波阵面或脉冲在主动分布式动力学系统中的传播可以由二阶半线性抛物微分方程或此类方程的系统描述[16]。在这种行为的现象学研究中，除了动力学理论之外，还发展了一种可激发介质的公理化理论[19，8，91]。与此相关的是，建立从动力学理论到公理理论的过渡是合理的条件，并从动力学方程的相应性质确定可激发介质的性质，这是有意义的。本文的目的是证明（在一定条件下）的有效性，这种通道的小扩散方程，描述的浓度波的传播，如果扩散系数趋于零。在稍微修改的假设下，这些结果在[lo]中没有详细证明就被宣布了。
The propagation of wave fronts or pulses in active distributed kinetic systems can be described by semi-linear parabolic differential equations of the second order or by systems of such equations [16]. In the phenomenological investigation of such behavior there has been developed, besides the kinetic theory, an axiomatic theory of excitable media [19, 8, 91. In connection with this it is of interest to establish conditions under which the passage from the kinetic theory to the axiomatic one is justified, and to determine properties of excitable media from the corresponding properties of the kinetic equations. The aim of the present paper is to prove (under certain conditions) the validity of such passage for equations with small diffusion, describing the propagation of concentration waves, if the diffusion coefficients tend to zero. Under slightly modified assumptions these results have been announced without detailed proof in [lo].