Introduction to reaction-diffusion equations : theory and applications to spatial ecology and evolutionary biology

Introduction to reaction-diffusion equations : theory and applications to spatial ecology and evolutionary biology / King-Yeung Lam, Yuan Lou.

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-par...

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Bibliographic Details
Main Authors: Lam, King-Yeung, 1985- (Author), Lou, Yuan, 1968- (Author)
Format: eBook
Language:English
Published: Cham : Springer, 2022.
Series:Lecture notes on mathematical modelling in the life sciences,
Subjects:
Reaction-diffusion equations.
Reaction-diffusion equations
Online Access:Click for online access
Table of Contents:
  • 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.

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