Title: Dynamics of hot spots in the logarithmic diffusion equation
Speaker: Eiji Yanagida (Tokyo Institute of Technology)
Abstract: This talk is concerned with the behavior of positive solutions to the logarithmic diffusion equation. It is known that due to fast diffusion of the equation, the extinction of solutions may occur in finite time. I will discuss the behavior of hot spots (maximum points) of solutions near the extinction time in the one-dimensional case. By applying the intersection number principle, it is shown that the hot spot typically converges to a point or goes to spatial infinity. However, in some cases, the hot spot remains bounded but does not converge to any particular point.
Seminar URL: https://research.math.osu.edu/pde/