SOME MAXIMUM PRINCIPLES FOR PARABOLIC MIXED LOCAL/NONLOCAL OPERATORS

Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci

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1 Citation (Scopus)

Abstract

The goal of this paper is to establish new Maximum Principles for parabolic equations in the framework of mixed local/nonlocal operators. In particular, these results apply to the case of mixed local/nonlocal Neumann boundary conditions, as introduced by Dipierro, Proietti Lippi, and Valdinoci [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp. 1093–1166]. Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect, which is performed by Dipierro, Proietti Lippi, and Valdinoci [J. Math. Biol. 89 (2024), Paper No. 19]. This is particularly relevant when studying biological populations, since the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction.

Original languageEnglish
Pages (from-to)3923-3939
Number of pages17
JournalProceedings of the American Mathematical Society
Volume152
Issue number9
DOIs
Publication statusPublished - Sept 2024

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