Introduction to Reaction-Diffusion Equations: Theory and Applications to Spatial Ecology and Evolutionary Biology

This book provides an introduction to basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It covers the maximum principle, principal eigenvalues, and Floquet bundles, as well as spatial ecology and evolutionary biology. It is aimed at graduate students and researchers interested in the theory and applications of reaction-diffusion equations.

Format: Paperback / softback
Length: 312 pages
Publication date: 02 December 2022
Publisher: Springer International Publishing AG

This comprehensive book delves into the realm of reaction-diffusion models, presenting a range of fundamental mathematical tools that have applications in spatial ecology and evolutionary biology. It is organized into four distinct parts, each designed to provide a thorough understanding of the subject matter.

In the first part, the reader is introduced to essential concepts such as the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. These foundational principles form the basis for further exploration in the subsequent parts of the book.

The second part focuses on the practical applications of reaction-diffusion models in spatial ecology. Here, the dynamics of a single species, as well as the interactions between two competing species, are examined in detail. Additionally, recent advancements in understanding the behavior of N competing species in bounded domains are discussed. Relevant results related to stream populations and phytoplankton populations are also included, providing a comprehensive overview of the field.

The third part delves into the realm of evolutionary biology, where reaction-diffusion models play a crucial role. The basic notions of adaptive dynamics, including evolutionarily stable strategies and evolutionary branching points, are introduced within the context of a competition model of stream populations. Furthermore, a class of selection-mutation models is explored, which describes a population structured along a continuous phenotypical trait.

To enhance the understanding of the theoretical foundations, the fourth part consists of several appendices. These appendices present a self-contained treatment of essential abstract theories in functional analysis and dynamical systems. Topics covered include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems.

Throughout the book, a strong emphasis is placed on self-containment, making it suitable for graduate students and researchers with a keen interest in the theory and applications of reaction-diffusion equations. The comprehensive nature of the content ensures that readers gain a deep understanding of the subject matter, enabling them to apply these mathematical tools to address complex ecological and evolutionary challenges.

Weight: 504g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031204210
Edition number: 1st ed. 2022