On the steady-states of a two-species non-local cross-diffusion model

• Autorzy: Rodríguez Nancy , Hu Yi

Identyfikatory

DOI

10.1515/jaa-2020-2003

• Języki publikacji: EN

Abstrakty

EN

We investigate the existence and properties of steady-state solutions to a degenerate, non-local system of partial differential equations that describe two-species segregation in homogeneous and heterogeneous environments. This is accomplished via the analysis of the existence and non-existence of global minimizers to the corresponding free energy functional. We prove that in the spatially homogeneous case global minimizers exist if and only if the mass of the potential governing the intra-species attraction is sufficiently large and the support of the potential governing the interspecies repulsion is bounded. Moreover, when they exist they are such that the two species have disjoint support, leading to complete segregation. For the heterogeneous environment we show that if a sub-additivity condition is satisfied then global minimizers exists. We provide an example of an environment that leads to the sub-additivity condition being satisfied. Finally, we explore the bounded domain case with periodic conditions through the use of numerical simulations.

Słowa kluczowe

EN

nonlocal equation; cross diffusion; energy minimizers

PL

równania nielokalne; dyfuzja wzajemna; minimalizator energii

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2020
• Tom: Vol. 26, nr 1
• Strony: 1--19
• Opis fizyczny: Bibliogr. 24 poz., wykr.

Twórcy

autor

Rodríguez Nancy

• Department of Applied Mathematics, University of Colorado Boulder, Engineering Center, ECOT 225, 526 UCB, Boulder, CO 80309-0526, USA

autor

Hu Yi

• Department of Electrical and Computer Engineering, Carnegie Mellon University Silicon Valley, 870 E El Camino Real, APT 171, Mountain View, CA 94040, USA

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).