A note on time-asymptotic bounds with a sharp algebraic rate and a transitional exponent for the sublinear Fujita problem

Abstract

This note establishes sharp time-asymptotic algebraic rate bounds for the classical evolution problem of Fujita, but with sublinear rather than superlinear exponent. A transitional stability exponent is identified, which has a simple reciprocity relation with the classical Fujita critical blow-up exponent.