Seminar 11.4.2019: Pavol Quittner

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 11.4.2019: Pavol Quittner

Postby quittner » Thu Apr 04, 2019 4:10 pm

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 11.4.2019 at 14:00 Lecture room M-223

Pavol Quittner (KAMŠ FMFI UK):
Entire solutions of a semilinear heat equation

Abstract:
We characterize some classes of positive entire solutions of the nonlinear heat equation $u_t=\Delta u+u^p$,
where $p$ is supercritical in the Sobolev sense. In particular, if $p>p_L$ where $p_L$ denotes the Lepin exponent,
then any positive entire radial solution has to be a steady state (the condition $p\geq p_L$ is known to be necessary for such statement).
As an application, we show the convergence of rescaled profiles of solutions with type II blow-up and of global solutions with slow time decay.
This is a joint work with Peter Poláčik (University of Minnesota).
quittner
 
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