Stability for Semilinear Parabolic Problems in $L_2$ and $W^{1,2}$

Pavel Gurevich; Martin Väth

doi:10.4171/zaa/1568

JournalszaaVol. 35, No. 3pp. 333–357

Stability for Semilinear Parabolic Problems in $L_{2}$ and $W^{1, 2}$

Pavel Gurevich
Freie Universität Berlin, Germany
Martin Väth
Czech Academy of Sciences, Prague, Czech Republic

$Stability for Semilinear Parabolic Problems in $L_2$ and $W^{1,2}$ cover$

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Abstract

Asymptotic stability is studied for semilinear parabolic problems in $L_{2} (Ω)$ and interpolation spaces. Some known results about stability in $W^{1, 2} (Ω)$ are improved for semilinear parabolic systems with mixed boundary conditions. The approach is based on Amann’s power extrapolation scales. In the Hilbert space setting, a better understanding of this approach is provided for operators satisfying Kato’s square root problem.

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Pavel Gurevich, Martin Väth, Stability for Semilinear Parabolic Problems in $L_{2}$ and $W^{1, 2}$ . Z. Anal. Anwend. 35 (2016), no. 3, pp. 333–357

DOI 10.4171/ZAA/1568