论文标题
非线性扩散的快速反应限制问题的自相似解决方案
Self-similar solutions of fast reaction limit problem with nonlinear diffusion
论文作者
论文摘要
在本文中，我们提出了一种表征非线性扩散系统的自相似快速反应极限的方法。对于适当的初始数据，在快速反应的极限中，随着k倾向于无限，空间隔离导致原始系统的两个组成部分会收敛到自相似极限限制曲线的正和负部分f（n），其中n = xt^（1/2）满足四个普通差异系统之一。通过使用侧重于a的射击方法（将溶液为正的区域分开且为负的区域）的射击方法，-phi（f）在n = a处分开的区域，k的位置是通过a的位置来证明，k的这些自相似解决方案的存在倾向于无限限制问题。自由边界的位置使我们对一种物质如何渗透到另一种物质中，对于非线性扩散的特定形式，也研究了非线性扩散形式与自由边界的位置之间的关系。
In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit as k tends to infinithy,spatial segregation results in the two components of the original systems converging to the positive and negative parts of a self-similar limit profile f (n), where n=xt^(1/2) that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the k tends to infinity limit problems is proved by using shooting methods which focus on a, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and g, the derivative of -phi(f) at n = a. The position of the free boundary gives us intuition about how one substance penetrates into the other, and for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied.
