
Nonlocal Diffusion Problems
American Mathematical Society (Publisher)
Will be published approx. on 30. October 2010
Book
Hardback
256 pages
978-0-8218-5230-9 (ISBN)
Description
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
Reviews / Votes
"The results of this book are given with complete proofs and also an emphasis on the intuitive understanding of the results. This extends the audience beyond mathematicians to include engineers, physicists and biologists with a good background in Analysis and PDEs."-- Mathematical Reviews
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Weight
645 gr
ISBN-13
978-0-8218-5230-9 (9780821852309)
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Schweitzer Classification