Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Seminar on Qualitative Theory of Differential Equations - Pavol Quittner (1.10.2020)

Thursday 1.10.2020 at 14:00, Lecture room C

21. 09. 2020 13.09 hod.
Od: Pavol Quittner

Pavol Quittner:
An optimal Liouville theorem for a semilinear heat equation

Liouville-type theorems for entire solutions of scaling invariant nonlinear parabolic equations and systems guarantee optimal universal estimates of solutions of related initial and initial-boundary value problems, including estimates of their singularities and decay.

In this talk I will first review known Liouville-type theorems for a semilinear heat equation (sometimes called the Fujita equation) and then I will give a sketch of the proof of a Liouville-type theorem guaranteeing the nonexistence of positive entire solutions of the Fujita equation in the full subcritical range.

Our approach can also be used for a class of semilinear parabolic systems and the linear heat equation with a nonlinear boundary condition.

More information