Stability for semilinear parabolic problems in L₂, W^1,2, and interpolation spaces

2014/09/15 by Pavel Gurevich, Gurevich, Pavel, Martin Väth +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP #math.DS #math.FA #msc:34G25 #msc:35K55 #msc:35K90 #msc:37L15

paper · pdf · doi:10.48550/arxiv.1409.4182

27 pages. New references added, structure changed

arxiv created 2015/04/13 · arxiv updated 2015/04/14

Abstract

An asymptotic stability result for parabolic semilinear problems in L₂(Ω) and interpolation spaces is shown. Some known results about stability in W^1,2(Ω) are improved for semilinear parabolic mixed boundary value problems. The approach is based on Amann's power extrapolation scales. In a Hilbert space setting, a better understanding of this approach is provided for operators satisfying Kato's square root problem; as a side result some equivalent characterizations of these operators are obtained.

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• Global Dynamics, Blow-Up, and Bianchi Cosmology

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