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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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Summary of main results for the PME/FDE

Summary of main results for the PME/FDE

Chapter:
(p.178) 10 Summary of main results for the PME/FDE
Source:
Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199202973.003.0011

This chapter reviews the results of the preceding chapters, paying special attention to the variation of the results and effects on the main parameters m and n. This is interpreted in terms of the different diffusion power and propagation speed associated to the equation when m varies. The idea of comparison with the heat equation and its Gaussian kernel is always present. The chapter ends with a complete review of the existence of the natural extension of this object, i.e., the existence of source solutions for the whole family PME/FDE with m = 1. The concept of background signal is introduced.

Keywords:   supercritical range, subcritical range, Dirac masses, background signal

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