Degenerate Cahn–Hilliard systems: From nonlocal to local-Reference-Cited by-同舟云学术

Degenerate Cahn–Hilliard systems: From nonlocal to local

Published:2024-08-31 Issue: Volume: Page:
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Carrillo José A.¹^ORCID,Elbar Charles²^ORCID,Skrzeczkowski Jakub¹³^ORCID

Affiliation:

1. Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK

2. Laboratoire Jacques-Louis Lions (LJLL), Faculté des Sciences et Ingénierie, Sorbonne Université, 4 place Jussieu, F-75005 Paris, France

3. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Stefana Banacha 2, 02-097 Warsaw, Poland

Abstract

We provide a rigorous mathematical framework to establish the limit of a nonlocal model of cell–cell adhesion system to a local model. When the parameter of the nonlocality goes to 0, the system tends to a Cahn–Hilliard system with degenerate mobility and cross-interaction forces. Our analysis relies on a-priori estimates and compactness properties.

Funder

European Research Council Executive Agency

EPSRC

"Maria de Maeztu" Excellence Unit IMAG

National Science Center, Poland

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021919972450041X

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