Ebook: Transport Equations in Biology
Author: Benoît Perthame (auth.)
- Tags: Mathematical Biology in General, Ordinary Differential Equations, Dynamical Systems and Ergodic Theory
- Series: Frontiers in Mathematics
- Year: 2007
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion).
Original mathematical methods described are, among others, the generalized relative entropy method - a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion).
Original mathematical methods described are, among others, the generalized relative entropy method - a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.
Content:
Front Matter....Pages i-ix
From differential equations to structured population dynamics....Pages 1-26
Adaptive dynamics; an asymptotic point of view....Pages 27-53
Population balance equations: the renewal equation....Pages 55-80
Population balance equations: size structure....Pages 81-110
Cell motion and chemotaxis....Pages 111-149
General mathematical tools....Pages 151-178
Back Matter....Pages 179-198
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion).
Original mathematical methods described are, among others, the generalized relative entropy method - a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.
Content:
Front Matter....Pages i-ix
From differential equations to structured population dynamics....Pages 1-26
Adaptive dynamics; an asymptotic point of view....Pages 27-53
Population balance equations: the renewal equation....Pages 55-80
Population balance equations: size structure....Pages 81-110
Cell motion and chemotaxis....Pages 111-149
General mathematical tools....Pages 151-178
Back Matter....Pages 179-198
....