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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

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

Juan Luis Vázquez

Oxford University Press

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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