Seminár z kvalitatívnej teórie diferenciálnych rovníc - Pavol Quittner (4.4.2019)
vo štvrtok 4.4.2019 o 14:00 hod. v miestnosti M/223
Prednášajúci: Pavol Quittner
Názov prednášky: Ancient and self-similar solutions of a semilinear heat equation
Termín: 4.4.2019, 14:00 hod., M/223
Abstrakt:
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).