Pavol Quittner

Comenius University

An optimal Liouville-type theorem for entire solutions of 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.