Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 4.4.2019 at 14:00 Lecture room M-223

Pavol Quittner (KAMŠ FMFI UK):

Ancient and self-similar solutions of a semilinear heat equation

Abstract:

We consider positive radially symmetric solutions of the nonlinear heat equation $u_t=\Delta u+u^p$, where $p>1$.

Ancient, and in particular backward self-similar solutions, play a crucial role in the study of blow-up. In addition,

they have also been used in the study of global solutions and in the construction of peaking and homoclinic solutions, for example.

In spite of an intensive and longstanding research, many basic questions on ancient and self-similar solutions remain open

and we will answer some of them.

This is a joint work with Peter Polacik (University of Minnesota).