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

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

(p.22) 2 Smoothing effect and time decay. Data in L 1 (Rn) or M (Rn)
Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Juan Luis Vázquez

Oxford University Press

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

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