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The Mathematics of Diffusion

The Mathematics of Diffusion

$61.00 (P)

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Date Published: October 2011
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9781611971965

$ 61.00 (P)
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion 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.

    • Major modern achievements are described in order to quickly bring readers to the cutting edge of the subject
    • Throughout the book many simple, fundamental and important open problems are mentioned with their significance explained
    • Suitable for use as a graduate student text or as a reference book for researchers
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    Product details

    • Date Published: October 2011
    • format: Paperback
    • isbn: 9781611971965
    • length: 128 pages
    • dimensions: 252 x 171 x 7 mm
    • weight: 0.22kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. Introduction: the heat equation
    2. Dynamics of general reaction-diffusion equations and systems
    3. Qualitative properties of steady states of reaction-diffusion equations and systems
    4. Diffusion in heterogeneous environments:
    2 x 2 Lotka–Volterra competition systems
    5. Beyond diffusion: directed movements, taxis, and cross-diffusion
    Bibliography
    Index.

  • Author

    Wei-Ming Ni, University of Minnesota
    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.

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