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Smoothing and Decay Estimates for Nonlinear Diffusion Equations
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Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Juan Luis Vázquez

Abstract

This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of physics, chemistry, biology, and engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity (equations of porous med ... More

Keywords: classical heat equation, nonlinearities of power type, singular parabolicity, decay rates, asymptotics, time decay, smoothing, extinction in finite time, delayed regularity

Bibliographic Information

Print publication date: 2006 Print ISBN-13: 9780199202973
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780199202973.001.0001

Authors

Affiliations are at time of print publication.

Juan Luis Vázquez, author
Universidad Autónoma de Madrid

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