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A doubly critical degenerate parabolic problem

โœ Scribed by Michael Winkler

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
107 KB
Volume
27
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Abstract

It is shown that the Dirichlet problem for

where ฮฉโŠ‚โ„__^n^__ is critical in that it has first eigenvalue one, is globally solvable for any continuous positive initial datum vanishing at __โˆ‚__ฮฉ. Moreover, for p<3 all solutions are bounded and tend to some nonnegative eigenfunction of the Laplacian as tโ†’โˆž, while if pโฉพ3 then there are both bounded and unbounded solutions. Finally, it is shown that unlike the case pโˆˆ[0,1), all steady states are unstable if pโฉพ1. Copyright ยฉ 2004 John Wiley & Sons, Ltd.

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