A study of dynamics of a traveling wave and a interface in nonlinear diffusion equations

非线性系统的扩散现象出现在物理、化学、生物学以及最近的金融工程等许多领域。在这些领域中，出现了被称为界面的局域化结构，在该界面处，状态的快速变化集中在狭窄的边界上，并且有很多理解该界面所表现出的行为成为澄清非线性现象的关键。行波解是构成该界面的一种特殊解。本文对非线性扩散现象中的界面动力学和行波动力学进行了数学分析。

The diffusion phenomenon of the nonlinear system appears in a lot of fields like physics, chemistry, biology, and recently, the financial engineering etc. In them, the localized structure that is called an interface where a rapid state variation concentrates on the narrow confine appears, and there are a lot that understanding the behavior that this interface shows becomes a key to clarify a nonlinear phenomenon. The traveling wave solution is a special solution that composes this interface. In the present study, the dynamics of the interface and the traveling wave in the nonlinear diffusion phenomenon was mathematically analyzed.