抛物线局部/非局部混合算子的一些最大原则

Pub Date : 2024-05-01 DOI:10.1090/proc/16899

Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci

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引用次数: 0

摘要

本文的目的是在混合局部/非局部算子的框架内建立抛物方程的新最大原则。特别是，这些结果适用于混合局部/非局部诺伊曼边界条件的情况，正如迪皮埃罗、普罗埃蒂-利皮和瓦尔迪诺奇所介绍的那样[Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp.］此外，它们在涉及所谓阿利效应的种群动态分析中也发挥着重要作用，迪皮埃罗、普罗埃蒂-利皮和瓦尔迪诺奇[J. Math. Biol. 89 (2024)，论文编号 19]对此进行了研究。在研究生物种群时，这一点尤为重要，因为阿利效应可以检测到一个临界密度，低于这个密度，种群就会严重濒危，面临灭绝的危险。

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Some maximum principles for parabolic mixed local/nonlocal operators

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.

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