Seminár z kvalitatívnej teórie diferenciálnych rovníc - Pavol Quittner (10.4.2025)

vo štvrtok 10.4.2025 o 14:00 hod. v miestnosti M 223

07. 04. 2025 21.39 hod.
Od: Pavol Quittner

Prednášajúci: Pavol Quittner

Názov prednášky: Threshold, subthreshold and global unbounded solutions of superlinear heat equations

Termín: 10.4.2025, 14:00 hod., M 223

Abstrakt:
We consider the semilinear heat equation with a superlinear nonlinearity and we study the properties of threshold or subthreshold solutions, lying on or below the boundary between blow-up and global existence, respectively. For the Cauchy-Dirichlet problem, we prove the boundedness of any subthreshold solution. This implies, in particular, that all global unbounded solutions - if they exist - are threshold solutions. For the Cauchy problem, these properties fail in general but we show that they become true for a suitably modified notion of threshold. Our results improve known results even in the special case of power nonlinearities, especially in the Sobolev critical and supercritical cases.

This is a joint work with Philippe Souplet.