Global solutions to semilinear parabolic equations driven by mixed local–nonlocal operators

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-11-26 DOI:10.1112/blms.13196

Stefano Biagi, Fabio Punzo, Eugenio Vecchi

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Abstract

We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local–nonlocal operator $L = - Δ + {(- Δ)}^{s}$ , with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian.