Measure Valued Solutions of the 2D Keller-Segel System

S. Luckhaus; Y. Sugiyama; J. J.L. Velázquez

doi:10.1007/s00205-012-0549-9

Measure Valued Solutions of the 2D Keller-Segel System

S. Luckhaus, Y. Sugiyama, J. J.L. Velázquez

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

We develop a theory of global measure-valued solutions for the classical Keller-Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller-Segel system are not globally defined in time.

Original language	English
Pages (from-to)	31-80
Number of pages	50
Journal	Archive for Rational Mechanics and Analysis
Volume	206
Issue number	1
DOIs	https://doi.org/10.1007/s00205-012-0549-9
Publication status	Published - Oct 2012

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-012-0549-9

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abstract = "We develop a theory of global measure-valued solutions for the classical Keller-Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller-Segel system are not globally defined in time.",

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Measure Valued Solutions of the 2D Keller-Segel System

Abstract

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