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The Mathematics of Diffusion

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by Wei-Ming Ni


2011 / xii + 108 pages / Softcover / ISBN 978-1-611971-96-5 / List Price $66.50 / SIAM Member Price $46.55 / Order Code CB82

Keywords: diffusion, directed movements, taxis, spatial heterogeneity, pattern formation


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.

This book is intended for researchers and graduate students in the areas of elliptic or parabolic equations and in mathematical biology.

About the Author
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.

ISBN 9781611971966

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