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arXiv · 2408.01577

Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation

L. Del Pezzo·R. Ferreira
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Abstract

In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator, \[ u_t=a\Delta u -b(-\Delta)^s u+u^p. \] We show that the Fujita exponent is given by the nonlocal part, $p_F=1+2s/N$. We also determinate, in some cases, the blow-up rate.

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L. Del Pezzo, R. Ferreira. 2024-08-02. Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation. https://doi.org/10.1016/j.na.2025.113761

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