Chapter

Improved analysis of the critical line. Delayed regularity

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/9780199202973.003.0007

Series: Oxford Lecture Series in Mathematics and Its Applications

 Improved analysis of the critical line. Delayed regularity

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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

Chapter.  4941 words. 

Subjects: Applied Mathematics

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