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Nonlocal Diffusion Problems (Hardcover)
Loot Price: R3,197
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Nonlocal Diffusion Problems (Hardcover)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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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.
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