The Mathematics of Diffusion
Will be published approx. on 30. September 2011
Book
Paperback/Softback
122 pages
978-1-61197-196-5 (ISBN)
Description
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. This book focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity.
The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical Lotka-Volterra competition systems.
Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate.
The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical Lotka-Volterra competition systems.
Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 260 mm
Width: 179 mm
Thickness: 10 mm
Weight
223 gr
ISBN-13
978-1-61197-196-5 (9781611971965)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Wei-Ming Ni holds a joint appointment as the Director of the Center for Partial Differential Equations at East China Normal University in Shanghai and as Professor of Mathematics at the University of Minnesota. His research interests include the qualitative properties of solutions to nonlinear elliptic and parabolic equations.
Content
Preface
Chapter 1. Introduction: The Heat Equation
Chapter 2. Dynamics of General Reaction-Diffusion Equations and Systems
Chapter 3. Qualitative Properties of Steady States of Reaction-Diffusion Equations and Systems
Chapter 4. Diffusion in Heterogeneous Environments: 2 x 2 Lotka-Volterra Competition Systems
Chapter 5. Beyond Diffusion: Directed Movements, Taxis, and Cross-Diffusion
Bibliography
Index.
Chapter 1. Introduction: The Heat Equation
Chapter 2. Dynamics of General Reaction-Diffusion Equations and Systems
Chapter 3. Qualitative Properties of Steady States of Reaction-Diffusion Equations and Systems
Chapter 4. Diffusion in Heterogeneous Environments: 2 x 2 Lotka-Volterra Competition Systems
Chapter 5. Beyond Diffusion: Directed Movements, Taxis, and Cross-Diffusion
Bibliography
Index.