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

TL;DR

This paper derives precise algebraic decay bounds for the sublinear Fujita problem, revealing a transitional stability exponent linked to the classical blow-up exponent, advancing understanding of long-term solution behavior.

Contribution

It introduces sharp time-asymptotic bounds for the sublinear Fujita problem and identifies a transitional stability exponent with a reciprocal relation to the classical blow-up exponent.

Findings

Established sharp algebraic decay bounds for sublinear Fujita evolution.

Identified a transitional stability exponent with a simple reciprocity relation.

Enhanced understanding of long-term solution behavior in sublinear Fujita problems.

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.