The Fujita phenomenon in exterior domains under the Robin boundary conditions

TL;DR

This paper investigates the Fujita phenomenon for nonlinear parabolic equations in exterior domains with Robin boundary conditions, identifying a critical exponent that determines whether solutions blow up or exist globally.

Contribution

It extends the understanding of the Fujita phenomenon to exterior domains with Robin boundary conditions, establishing the critical exponent and solution behaviors.

Findings

Existence of a critical exponent p = 1+2/N for blow-up versus global solutions.

Blow-up occurs for subcritical exponents regardless of initial data.

Global solutions can exist for small initial data in the supercritical case.

Abstract

The Fujita phenomenon for nonlinear parabolic problems dtu = \deltau + up in an exterior domain of RN under the Robin boundary conditions is investigated in the superlinear case. As in the case of Dirichlet boundary conditions, it turns out that there exists a critical exponent p = 1+2/N such that blow-up of positive solutions always occurs for subcritical exponents, whereas in the supercritical case global existence can occur for small non-negative initial data.