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

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.

27 pages. New references added, structure changed

Cited by in corpus (1)

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