Journal article
L∞ estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems
- Abstract:
- We prove L∞ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial L∞ norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian solutions without the diffusive term by characteristic methods.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 157.6KB, Terms of use)
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- Publisher copy:
- 10.1090/qam/1493
Authors
- Publisher:
- American Mathematical Society
- Journal:
- Quarterly of Applied Mathematics More from this journal
- Volume:
- 76
- Issue:
- 3
- Pages:
- 515-530
- Publication date:
- 2017-11-07
- Acceptance date:
- 2017-09-22
- DOI:
- EISSN:
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1552-4485
- ISSN:
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0033-569X
- Language:
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English
- Keywords:
- Pubs id:
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1098244
- Local pid:
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pubs:1098244
- Deposit date:
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2020-04-07
- ARK identifier:
Terms of use
- Copyright holder:
- Brown University
- Copyright date:
- 2018
- Rights statement:
- © 2017 Brown University.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from the American Mathematical Society at: https://doi.org/10.1090/qam/1493
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