Mathematical Models and Methods in Applied Sciences· 2015Q1
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
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- Q1SCImago
- 2015year
Short summary
This paper surveys and critically analyzes Keller–Segel chemotaxis models, focusing on preventing non-physical solution blow-ups and deriving macroscopic models from kinetic theory.
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Key points
- Surveys and critically analyzes Keller–Segel chemotaxis models and their modifications.
- Focuses on models designed to prevent non-physical blow-ups of solutions.
- Examines the existence, blow-up, and asymptotic behavior of model solutions.
- Derives macroscopic models from kinetic theory, including classical and new models.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.
The authors' abstract, as published at the source. Mathematical Models and Methods in Applied Sciences, 2015 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics