题目:Front dynamics and entire solutions to reaction-diffusion equations

演讲人：Professor Yoshihisa Morita (Ryukoku University, Japan, morita@rins.ryukoku.ac.jp)

时间：2008年10月23日（星期四）下午3：00-4：00

地点：闵行数学楼102报告厅

Abstract: It is interesting to study propagation phenomena modeled by reaction-diffusion equations in various fields of materials science, biology and life science. Corresponding to a wave propagation, the equations allow a traveling wave that has a constant profile and a constant speed. Here we consider a simple model equation, that is a scalar reaction-diffusion equation of one-space dimension $u_t=u_{xx}+f(u)$ with a bistable condition. It is known that the equation allows 6 types of monotone traveling waves (traveling fronts), counting the solutions obtained by the reflection in the space. In addition to the traveling fronts, we can also observe interacting behavior of two fronts. In this talk we show the existence of entire solutions which behaves in the way two traveling fronts are coming or diverging. Here an entire solution is meant by a classical solution defined for all $x$ and $t$. Although an equilibrium solution and a traveling wave solution are examples of entire solutions, our entire solutions are different from those and exhibit characteristic behaviors in the front dynamics.