Stability for semilinear parabolic problems in L2, W1,2, and interpolation spaces
Abstract
An asymptotic stability result for parabolic semilinear problems in L2() and interpolation spaces is shown. Some known results about stability in W1,2() 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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