Uniform in time L∞-estimates for nonlinear aggregation-diffusion equations
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Accepted version
Author(s)
Carrillo, JA
Wang, J
Type
Journal Article
Abstract
We derive uniform in time L∞-bound for solutions to an aggregation-diffusion model with attractive-repulsive potentials or fully attractive potentials. We analyze two cases: either the repulsive nonlocal term dominates over the attractive part, or the diffusion term dominates over the fully attractive nonlocal part. When the repulsive part of the potential has a weaker singularity (2 − n≤ B< A≤ 2), we use the classical approach by the Sobolev and Young inequalities together with differential iterative inequalities to prove that solutions have the uniform in time L∞-bound. When the repulsive part of the potential has a stronger singularity (− n< B< 2 − n≤ A≤ 2), we show the uniform bounds by utilizing properties of fractional operators. We also show uniform bounds in the purely attractive case 2 − n≤ A≤ 2 within the diffusion dominated regime.
Date Issued
2019-12-01
Date Acceptance
2018-10-21
Citation
Acta Applicandae Mathematicae, 2019, 164 (1), pp.1-19
ISSN
0167-8019
Publisher
Springer
Start Page
1
End Page
19
Journal / Book Title
Acta Applicandae Mathematicae
Volume
164
Issue
1
Copyright Statement
© 2018 Springer-Verlag. The final publication is available at Springer via https://dx.doi.org/10.1007/s10440-018-0221-y
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P031587/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Aggregation-diffusion equations
Global in time uniform estimates
Stroock-Varopoulos inequality
KELLER-SEGEL MODEL
GLOBAL EXISTENCE
BLOW-UP
General Mathematics
0102 Applied Mathematics
0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2018-10-26