Journal article

Splitting schemes and segregation in reaction cross-diffusion systems

Abstract:: One of the most fascinating phenomenon observed in reaction diffusion systems is the emergence of segregated solutions, i.e., population densities with disjoint supports. We analyze such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction of their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Carrillo, J. A., Fagioli, S., Santambrogio, F., & Schmidtchen, M. (2018). Splitting schemes and segregation in reaction cross-diffusion systems. SIAM Journal on Applied Mathematics , 50(5), 5695–5718.

MLA Style

Carrillo, J. A., et al. “Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems.” SIAM Journal on Applied Mathematics , vol. 50, no. 5, Society for Industrial and Applied Mathematics , 2018, pp. 5695–718.

Chicago Style

Carrillo, JA, S Fagioli, F Santambrogio, and M Schmidtchen. 2018. “Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems.” SIAM Journal on Applied Mathematics 50 (5): 5695–5718.
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Files:: 17m1158379.pdf

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Publisher copy:: 10.1137/17M1158379

Authors

+ Carrillo, JA More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Fagioli, S More by this author

Role:: Author

+ Santambrogio, F More by this author

Role:: Author

+ Schmidtchen, M More by this author

Role:: Author

Publisher:: Society for Industrial and Applied Mathematics
Journal:: SIAM Journal on Applied Mathematics More from this journal
Volume:: 50
Issue:: 5
Pages:: 5695-5718
Publication date:: 2018-10-30
Acceptance date:: 2018-08-16
DOI:: 10.1137/17M1158379
EISSN:: 1095-7154
ISSN:: 0036-1410

Language:: English
Keywords:: segregation

FFR

splitting schemes

pattern formation

cross-diffusion

reaction diffusion

variational schemes
Pubs id:: 1098240
Local pid:: pubs:1098240
Deposit date:: 2020-04-07

Terms of use

Copyright holder:: Society for Industrial and Applied Mathematics
Copyright date:: 2018
Rights statement:: © 2018, Society for Industrial and Applied Mathematics. Published by SIAM under the terms of the Creative Commons 4.0 license

Licence:: CC Attribution (CC BY)

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