Extinction rates and asymptotics for 0 < <i>m</i> < <i>m</i> <sub> <i>c</i> </sub>

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:

Series: Oxford Lecture Series in Mathematics and Its Applications

 Extinction rates and asymptotics for 0 < m < m  c

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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

Chapter.  12969 words.  Illustrated.

Subjects: Applied Mathematics

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