Journal article
Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
- Abstract:
- We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 809.8KB, Terms of use)
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- Publisher copy:
- 10.1137/19M125827X
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Applied Mathematics More from this journal
- Volume:
- 80
- Issue:
- 1
- Pages:
- 232-261
- Publication date:
- 2020-01-16
- Acceptance date:
- 2019-10-28
- DOI:
- EISSN:
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1095-712X
- ISSN:
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0036-1399
- Language:
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English
- Keywords:
- Pubs id:
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1098217
- Local pid:
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pubs:1098217
- Deposit date:
-
2020-04-07
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2020
- Rights statement:
- © 2020, Society for Industrial and Applied Mathematics.
- Notes:
- This is the publisher's version of the article. The final version is available online from the Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/19M125827X
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