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Title
Introduction to reaction-diffusion equations : theory and applications to spatial ecology and evolutionary biology / King-Yeung Lam, Yuan Lou.
ISBN
9783031204227 (electronic bk.)
3031204220 (electronic bk.)
3031204212
9783031204210
Published
Cham : Springer, 2022.
Language
English
Description
1 online resource (xvi, 312 pages) : illustrations
Item Number
10.1007/978-3-031-20422-7 doi
Call Number
QA377
Dewey Decimal Classification
515/.3534
Summary
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 8, 2022).
Series
Lecture notes on mathematical modelling in the life sciences, 2193-4797
Available in Other Form
Print version: 9783031204210
Part I Linear Theory
1. The Maximum Principle and the Principal Eigenvalues for Single Equations
2. The Principal Eigenvalue for Periodic-Parabolic Problems
3. The Maximum Principle and the Principal Eigenvalue for Systems
4. The Principal Floquet Bundle for Parabolic Equations
Part II Ecological Dynamics
5. The Logistic Equation With Diffusion
6. Spreading in Homogeneous and Shifting Environments
7. The Lotka-Volterra Competition-Diffusion Systems for Two Species
8. Dynamics of Phytoplankton Populations
Part III Evolutionary Dynamics
9. Elements of Adaptive Dynamics
10. Selection-Mutation Models
Part IV Appendices
A. The Fixed Point Index
B. The Krein-Rutman Theorem
C. Subhomogeneous Dynamics
D. Existence of Connecting Orbits
E. Abstract Competition Systems in Ordered Banach Spaces
Index.
