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Smoothing and Decay Estimates for Nonlinear Diffusion EquationsEquations of Porous Medium Type$
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Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

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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Improved analysis of the critical line. Delayed regularity

Improved analysis of the critical line. Delayed regularity

Chapter:
(p.107) 6 Improved analysis of the critical line. Delayed regularity
Source:
Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199202973.003.0007

This chapter continues the analysis of the functional properties of the evolution semigroup generated by the FDE on the critical line, i.e., when m < mc and p assumes the critical value p* = n(1 - m)/2. The question addressed is boundedness, i.e., finding conditions on u0 under which function u(·, t) is bounded for all t > 0. The phenomenon of delayed regularity and immediate boundedness are discussed.

Keywords:   delayed regularity, immediate boundedness, semigroup, FDE

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