Parabolic Equations in Biology
Growth, reaction, movement and diffusion
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Beschreibung
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
Provides the basic content for a course at master level on fundamental models in mathematics used for modeling in biology Includes applications to ecology and population dynamics, neurosciences, enzymatic reactions and chemotaxis Presents an original and rigorous presentation of several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations
Autor*in
Benoît Perthame
Themen in »Parabolic Equations in Biology«
Fokker-Planck equations Mathematical biology Reaction-diffusion Traveling waves Turing patterns
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“This book presents a variety of phenomena arising in the analysis of partial differential equations modelling of biological, physical and chemical processes. … This book can well serve as a textbook for a course on master's level. Exercise problems are given in each chapter.” (Jonathan Zinsl, zbMATH 1333.35001, 2016)
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