(Non)local logistic equations with Neumann conditions

By Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci. Annales de l'Institut Henri Poincare. Analyse non linéar, 2021

144 citations recorded by the source corpus.

Abstract. We consider here a problem of population dynamics modeled on a logistic equation with both classical and nonlocal diffusion, possibly in combination with a pollination term. The environment considered is a niche with zero-flux, according to a new type of Neumann condition. We discuss the situations that are more favorable for the survival of the species, in terms of the first positive eigenvalue. Quite surprisingly, the eigenvalue analysis for the one dimensional case is structurally different than the higher dimensional setting, and it sensibly depends on the nonlocal character of the dispersal. The mathematical framework of this problem takes into consideration the equation −α∆u+ β(−∆)u = (m− μu)u+ τ J ⋆ u in Ω,

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/613cb6ce40b0450ff48f72bb1a7e061c7b970db4

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Citations in the corpus

Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, methodology): “We also refer to Biagi-Dipierro-Valdinoci-Vecchi [4, 8], Dipierro-RosOton-Serra-Valdinoci [22], Dipierro-Proietti Lippi-Valdinoci [21], Dipierro-Valdinoci [23] and the references therein.”
Regularity results for solutions of mixed local and nonlocal elliptic equations (2022, background): “The analysis of different types of mixed operators motivated by biological questions has also carried out in [19, 26, 27].”
On the regularity theory for mixed local and nonlocal quasilinear elliptic equations (2021, methodology): “16) have recently been studied by Biagi-Dipierro-Valdinoci-Vecchi [6,7], Dipierro-Proietti Lippi-Valdinoci [22,23] and Dipierro-Ros-Oton-Serra-Valdinoci [24].”
A Brezis-Nirenberg type result for mixed local and nonlocal operators (2022, unknown): “…subject of investigation, arising naturally in several ﬁelds, for instance as the super-position of diﬀerent types of stochastic processes such as a classical random walk and a L´evy ﬂight, which has also interesting application in the study of optimal animal foraging strategies, see [20,21,26,28].”
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, methodology): “Furthermore, existence, regularity, symmetry and maximum principles along various qualitative properties of solutions have been recently investigated by Biagi-DipierroValdinoci-Vecchi [12, 13], Dipierro-Proietti Lippi-Valdinoci [35, 36], Biagi-Mugnai-Vecchi [15], Dipierro-Ros-Oton-Serra-Valdinoci [3”
Linear theory for a mixed operator with Neumann conditions (2020, unknown): “More speciﬁcally, in [37] a biological population was taken into consideration within an environment which could be partially hostile.”
A Faber-Krahn inequality for mixed local and nonlocal operators (2021, background): “Further applications arise in the theory of optimal searching strategies, biomathe-matics and animal foraging; see [30, 31] and the references therein.”