Some maximum principles for parabolic mixed local/nonlocal operators

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-05-01 DOI:10.1090/proc/16899

Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci

引用次数: 0

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.

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抛物线局部/非局部混合算子的一些最大原则

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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