局部-非局部混合算子驱动的半线性抛物方程的全局解

IF 0.9 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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摘要

研究了由混合局部-非局部算子L = - Δ + （- Δ） s驱动的半线性抛物方程的Cauchy问题$\mathcal {L}= -\Delta +(-\Delta)^s$，具有类似幂的源项。我们证明了所谓的藤田现象是成立的，并且临界值与分数阶拉普拉斯式完全相同。

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

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.