Global and nonglobal solutions for a mixed local-nonlocal heat equation

TL;DR

This paper investigates the conditions under which solutions to a mixed local-nonlocal heat equation exist globally or blow up, recovering known critical exponents and extending understanding of such equations.

Contribution

It establishes optimal existence conditions for solutions of a semilinear parabolic equation with mixed operators, including the recovery of the Fujita exponent.

Findings

Derived optimal conditions for global solutions.

Identified criteria for solution blow-up.

Reproduced the Fujita exponent in this context.

Abstract

In this work, we establish optimal conditions concerning the global and nonglobal existence of solutions of a semilinear parabolic equations governed by a mixed local-nonlocal operator. Furthermore, our findings recover the Fujita exponent recently derived by Biagi, Punzo and Vecchi, as well as by Del Pezzo and Ferreira.