Blow up analysis for Keller-Segel system
Hua Chen, Jian-Meng Li, Kelei Wang
TL;DR
This paper develops a blow-up theory for the Keller-Segel system, analyzing singularities and solution structures, advancing understanding of its blow-up behavior and large-scale properties.
Contribution
It introduces a blow-up analysis framework for the Keller-Segel system, connecting it to Liouville equation insights and characterizing solution limits and structures.
Findings
Description of blow-up limits for the Keller-Segel system
Characterization of large-scale structure of solutions
Analysis of first-time singularities and ancient solutions
Abstract
In this paper we develop a blow up theory for the parabolic-elliptic Keller-Segel system, which can be viewed as a parabolic counterpart to the Liouville equation. This theory is applied to the study of first time singularities, ancient solutions and entire solutions, leading to a description of the blow-up limit in the first problem, and the large scale structure in the other two problems.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Biology Tumor Growth · Gene Regulatory Network Analysis · Markov Chains and Monte Carlo Methods