余维1子空间支持下具有分段常数产生的反应扩散方程组的精确行波解
Exact travelling solution for a reaction-diffusion system with a piecewise constant production supported by a codimension-1 subspace
摘要：
反应扩散系统的推广和他们的旅行解决方案的情况下，生产的一部分反应只发生在一个表面上的空间或平面上的一条线，但降解和扩散发生在散装是重要的模拟各种生物过程。这些问题包括入侵物种沿生态区边界的传播问题，在这种情况下，基因传播的问题，在腔中的形态发生，细胞内反应等。分段线性逼近的反应项在反应扩散系统中往往导致传播前沿问题的精确解。本文给出了一类具有余维1子集的分段常数产生的反应扩散方程组的精确行波解。解是单调的，以唯一的恒定速度传播，并将平凡解连接到问题的非平凡非齐次稳态解。该解的性质与经典反应扩散方程组的单调行波解的性质十分相似。
英文摘要：
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk are important for modelling various biological processes. These include problems of invasive species propagation along boundaries of ecozones, problems of gene spread in such situations, morphogenesis in cavities, intracellular reaction etc. Piecewise linear approximations of reaction terms in reaction-diffusion systems often result in exact solutions of propagation front problems. This article presents an exact travelling solution for a reaction-diffusion system with a piecewise constant production restricted to a codimension-1 subset. The solution is monotone, propagates with the unique constant velocity, and connects the trivial solution to a nontrivial nonhomogeneous stationary solution of the problem. The properties of the solution closely parallel the properties of monotone travelling solutions in classical bistable reaction-diffusion systems.
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