Fast Diffusion Limit for Reaction-Diffusion Systems with Stochastic Neumann Boundary Conditions
Fast Diffusion Limit for Reaction-Diffusion Systems with Stochastic Neumann Boundary Conditions
复制标题
具有随机诺依曼边界条件的反应扩散系统的快速扩散极限
DOI：
10.1137/140981952
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
W. W.Mohammed
中科院分区：
文献类型：
--
作者：
D. Blömker;W. W.Mohammed
考虑一类边界上带有随机扰动的反应扩散方程。我们表明，在快速扩散的限制，可以严格近似的随机Neumann边界条件的偏微分方程系统的解决方案，一个合适的随机/确定性微分方程的平均浓度，只涉及反应的解决方案。当边界上的噪声不改变平均浓度但足够大时，会发生有趣的效应。这里由于噪声的存在，令人惊讶的新的有效反应项可能出现在极限中。为了研究这种现象，我们专注于系统的多项式非线性，并说明它与简化，有点人工，例子，即，一个二维的非线性热方程和两种化学品之间的立方自催化反应。
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary conditions by the solution of a suitable stochastic/deterministic differential equation for the average concentration that involves reactions only. An interesting effect occurs in case the noise on the boundary does not change the averaging concentration but is sufficiently large. Here due to the presence of noise surprising new effective reaction terms may appear in the limit. To study this phenomenon we focus on systems with polynomial nonlinearities and illustrate it with simplified, somewhat artificial, examples, namely, a two-dimensional nonlinear heat equation and the cubic autocatalytic reaction between two chemicals.