Seminar on Qualitative Theory of Differential Equations - Pavol Quittner (4.4.2019)
Thursday 4.4.2019 at 14:00, Lecture room M/223
Pavol Quittner:
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).