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2003 Dynamics of parabolic equations: from classical solutions to metasolutions
Julián López-Gómez
Differential Integral Equations 16(7): 813-828 (2003). DOI: 10.57262/die/1356060598


In this paper we describe the asymptotic behavior of the positive solutions of a class of parabolic equations according to the size of a certain parameter. Within the range of values of the parameter where the model does not admit an attracting classical steady state it possesses an attracting metasolution ---a very weak generalized solution. It turns out that the minimal metasolution attracts all positive solutions starting in a subsolution and that the limiting profile of any other positive solution lies in the order interval defined by the minimal and the maximal metasolution.


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Julián López-Gómez. "Dynamics of parabolic equations: from classical solutions to metasolutions." Differential Integral Equations 16 (7) 813 - 828, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1036.35080
MathSciNet: MR1988726
Digital Object Identifier: 10.57262/die/1356060598

Primary: 35K55
Secondary: 35B30 , 35B40 , 35K20 , 37L30

Rights: Copyright © 2003 Khayyam Publishing, Inc.


Vol.16 • No. 7 • 2003
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