Chapter

Smoothing effect and time decay. Data in <i>L</i> <sup>1</sup> (R<sup> <i>n</i> </sup>) or <i>M</i> (R<sup> <i>n</i> </sup>)

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Published in print August 2006 | ISBN: 9780199202973
Published online September 2007 | e-ISBN: 9780191707919 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780199202973.003.0003

Series: Oxford Lecture Series in Mathematics and Its Applications

 Smoothing effect and time decay. Data in L 1 (R n ) or M (R n )

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This chapter discusses the smoothing and decay effects for the porous medium equation, using as a model case the famous Barenblatt solutions that have explicit formulas. Topics covered include source-type solutions, smoothing effect and decay with L 1 functions or measures as data, smoothing exponents and scaling properties, strong and weak smoothing effects, comparison for different diffusivities, a general smoothing result, and estimating the smoothing effect into Lp .

Keywords: smoothing effect; PME; Barenblatt solutions; source type solutions; decay; scaling properties; diffusivities

Chapter.  10171 words.  Illustrated.

Subjects: Applied Mathematics

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