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

Abstract

Asymptotic stability is studied for semilinear parabolic problems in $L_2(\Omega )$ and interpolation spaces. Some known results about stability in $W^{1,2}(\Omega )$ 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.