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Smoothing and Decay Estimates for Nonlinear Diffusion EquationsEquations of Porous Medium Type$
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Juan Luis Vázquez

Print publication date: 2006

Print ISBN-13: 9780199202973

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199202973.001.0001

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Preliminaries

Preliminaries

Chapter:
(p.9) 1 Preliminaries
Source:
Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199202973.003.0002

This chapter provides necessary preliminaries on functional analysis, comparison results, and the fundamentals of the PME. Section 1.2 provides the basic information on the equation that will serve as background material for the book. The some comparison results are presented. These results are discussed in more detail and the main facts are recalled in Section 1.3, since they are essential in the derivation of the estimates. Additional information is supplied in the appendices at the end.

Keywords:   functional analysis, comparison results, PME, Schwarz symmetrization, mass concentration

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