Nonlinear degenerate cross-diffusion systems with nonlocal interaction

Di Francesco M, Esposito A, Fagioli S (2018)

Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2018

Journal

Nonlinear Analysis - Theory Methods & Applications Elsevier

Publisher: PERGAMON-ELSEVIER SCIENCE LTD

Book Volume: 169

Pages Range: 94-117

DOI: 10.1016/j.na.2017.12.003

Abstract

We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan-Kinderlehrer-Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure. (C) 2017 Elsevier Ltd. All rights reserved.

Authors with CRIS profile

Antonio Esposito Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of L'Aquila / Università degli Studi dell'Aquila IT Italy (IT)

How to cite

APA:

Di Francesco, M., Esposito, A., & Fagioli, S. (2018). Nonlinear degenerate cross-diffusion systems with nonlocal interaction. Nonlinear Analysis - Theory Methods & Applications, 169, 94-117. https://doi.org/10.1016/j.na.2017.12.003

MLA:

Di Francesco, Marco, Antonio Esposito, and Simone Fagioli. "Nonlinear degenerate cross-diffusion systems with nonlocal interaction." Nonlinear Analysis - Theory Methods & Applications 169 (2018): 94-117.

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