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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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ONE-DIMENSIONAL THEORY. REGULARITY AND INTERFACES

ONE-DIMENSIONAL THEORY. REGULARITY AND INTERFACES

Chapter:
(p.357) 15 ONE-DIMENSIONAL THEORY. REGULARITY AND INTERFACES
Source:
The Porous Medium Equation
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198569039.003.0015

This chapter presents an introduction to some of the main topics relating to the PME, focusing on non-negative solutions. Section 15.1 presents a detailed analysis of the regularity of the pressure, for which Lipschitz continuity is proved both in space and time. Section 15.2 introduces new comparison results. Shifting comparison, intersection comparison and lap number count are quite useful in the study of interfaces. The study of interfaces is begun in Section 15.3. The growth of the interface is estimated and the waiting time analysed. Section 15.4 deals with some of the main issues of the theory.

Keywords:   PME, Cauchy problem, comparison theorems, interfaces, Lipschitz continuity

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