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L-infinity estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems

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Title: L-infinity estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems
Authors: Carrillo, J-A
Santambrogio, F
Item Type: Journal Article
Abstract: We prove $ L^\infty $ 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^\infty $ 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.
Issue Date: 1-Sep-2018
Date of Acceptance: 1-Sep-2017
URI: http://hdl.handle.net/10044/1/60430
DOI: https://dx.doi.org/10.1090/qam/1493
ISSN: 0033-569X
Publisher: American Mathematical Society
Start Page: 515
End Page: 530
Journal / Book Title: Quarterly of Applied Mathematics
Volume: 76
Issue: 3
Copyright Statement: © Copyright 2017 Brown University. First published in Quarterly of Applied Mathematics in 76 (2018), 515-530, published by the American Mathematical Society.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
MONGE-AMPERE EQUATION
GRADIENT FLOW
TIME AGGREGATION
CRITICAL MASS
MODEL
R-2
CHEMOTAXIS
ENERGY
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Online Publication Date: 2017-11-07
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences