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arXiv · 2406.17731

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

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 $\mathcal{L} = -\Delta+(-\Delta)^s$, 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.

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Stefano Biagi, Fabio Punzo, Eugenio Vecchi. 2024-06-25. Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators. https://arxiv.org/abs/2406.17731

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