Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on R-d, d >= 3

Eric A Carlen; Suleyman Ulusoy

doi:10.1016/j.na.2021.112314

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Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on R-d, d >= 3

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Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on R-d, d >= 3

Eric A Carlen and Suleyman Ulusoy

Nonlinear analysis, Vol.208

07/01/2021

DOI: https://doi.org/10.1016/j.na.2021.112314

Abstract

Mathematics

Mathematics, Applied

Physical Sciences

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We study an evolution equation that is the gradient flow in the 2-Wasserstein metric of a non-convex functional for densities in R-d with d >= 3. Like the Patlack- Keller-Segel system on R-2, this evolution equation features a competition between the dispersive effects of diffusion, and the accretive effects of a concentrating drift. We determine a parameter range in which the diffusion dominates, and all mass leaves any fixed compact subset of R-d at an explicit polynomial rate. (C) 2021 Elsevier Ltd. All rights reserved.

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Title: Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on R-d, d >= 3
Creators: Eric A Carlen - Rutgers, The State University of New Jersey
Suleyman Ulusoy - American University of Ras Al Khaimah
Publication Details: Nonlinear analysis, Vol.208
Date published: 07/01/2021
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Number of pages: 13
Grant note: DMS 1501007 / U.S. N.S.F. grant; National Science Foundation (NSF)
Academic Unit: Mathematics (SAS)
Language: English
Resource Type: Journal article
Identifiers: 991031716844104646