Stability for semilinear parabolic problems in $L_2$, $W^{1,2}$, and interpolation spaces

Pavel Gurevich; Martin Väth

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arXiv · 1409.4182

Stability for semilinear parabolic problems in $L_2$, $W^{1,2}$, and interpolation spaces

Pavel Gurevich·Martin Väth

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Abstract

An asymptotic stability result for parabolic semilinear problems in $L_2(\Omega)$ and interpolation spaces is shown. Some known results about stability in $W^{1,2}(\Omega)$ 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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Pavel Gurevich, Martin Väth. 2014-09-15. Stability for semilinear parabolic problems in $L_2$, $W^{1,2}$, and interpolation spaces. https://arxiv.org/abs/1409.4182

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