Stability for semilinear parabolic problems in L2 and W1,2

Asymptotic stability is studied for semilinear parabolic problems in L2(Ω) and interpolation spaces. Some known results about stability inW1,2(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. © European Mathematical Society.