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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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Extinction rates and asymptotics for 0 < m < m c

Extinction rates and asymptotics for 0 < m < m c

Chapter:
(p.116) 7 Extinction rates and asymptotics for 0 < m < m c
Source:
Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199202973.003.0008

This chapter deals with the actual asymptotic behaviour of the solutions of the FDE in the exponent range 0 < m < mc . This behaviour depends on the class of initial data. The chapter is interested in ‘small solutions’ that extinguish in finite time, according to the results of Chapter 5. It concentrates on solutions that start with initial data in L 1(R n), or solutions that fall into this class for positive times prior to extinction. In the range m < mc the ZKB solutions provide the clue to the asymptotics for all non-negative solutions with L 1-data.

Keywords:   extinction, self-similarity, radial asymptotic convergence, FDE, Yamabe flow, asymptotic behaviour, Dirichlet problem

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