Asymptotic stability is studied for semilinear parabolic problems in and interpolation spaces. Some known results about stability in 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.
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Pavel Gurevich, Martin Väth, Stability for Semilinear Parabolic Problems in and . Z. Anal. Anwend. 35 (2016), no. 3, pp. 333–357DOI 10.4171/ZAA/1568