Localization for a porous medium type equation in high dimensions
Authors:
Changfeng Gui and Xiaosong Kang
Journal:
Trans. Amer. Math. Soc. 356 (2004), 4273-4285
MSC (2000):
Primary 35K15, 35K55, 35K65; Secondary 35J40
DOI:
https://doi.org/10.1090/S0002-9947-04-03613-X
Published electronically:
May 28, 2004
MathSciNet review:
2067119
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove the strict localization for a porous medium type equation with a source term, ,
,
,
,
in the case of arbitrary compactly supported initial functions
. We also otain an estimate of the size of the localization in terms of the support of the initial data
and the blow-up time
. Our results extend the well-known one dimensional result of Galaktionov and solve an open question regarding high dimensions.
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Additional Information
Changfeng Gui
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email:
gui@math.uconn.edu
Xiaosong Kang
Affiliation:
The Fields institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Email:
xkang@fields.utoronto.ca
DOI:
https://doi.org/10.1090/S0002-9947-04-03613-X
Keywords:
Porous medium type equation with source,
localization property,
blow-up,
self-similar solutions,
comparison
Received by editor(s):
September 18, 2002
Published electronically:
May 28, 2004
Article copyright:
© Copyright 2004
American Mathematical Society