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The Porous Medium EquationMathematical Theory$
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Juan Luis Vazquez

Print publication date: 2006

Print ISBN-13: 9780198569039

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198569039.001.0001

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PRELIMINARIES AND BASIC ESTIMATES

PRELIMINARIES AND BASIC ESTIMATES

Chapter:
(p.30) 3 PRELIMINARIES AND BASIC ESTIMATES
Source:
The Porous Medium Equation
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198569039.003.0003

This chapter provides preliminary material on parabolic equations needed to develop the main theories of the book. It begins with a review of useful properties of quasilinear parabolic equations. Section 3.2 is devoted to non-degenerate versions of the generalized PME that will be used in approximating the degenerate cases. Section 3.3 focuses on properties that are formally satisfied by the PME; they will be justified in later chapters and used in the constructions of the different theories. Finally, Section 3.4 reviews the properties of the most popular alternative formulations of the PME.

Keywords:   PME, quasilinear parabolic equations, boundedness estimates, stability estimate, energy identity, time derivative

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