Uniform in time L∞-estimates for nonlinear aggregation-diffusion equations

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Title: Uniform in time L∞-estimates for nonlinear aggregation-diffusion equations
Authors: Carrillo, JA
Wang, J
Item 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.
Issue Date: 1-Dec-2019
Date of Acceptance: 21-Oct-2018
URI: http://hdl.handle.net/10044/1/64390
DOI: 10.1007/s10440-018-0221-y
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/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: 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
Online Publication Date: 2018-10-26
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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