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Zeitschrift für Analysis und ihre Anwendungen

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Volume 35, Issue 3, 2016, pp. 333–357
DOI: 10.4171/ZAA/1568

Published online: 2016-09-13

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

Pavel Gurevich[1] and Martin Väth[2]

(1) Freie Universität Berlin, Germany
(2) Czech Academy of Sciences, Prague, Czech Republic

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.

Keywords: Asymptotic stability, existence, uniqueness, parabolic PDE, strongly accretive operator, sesquilinear form, fractional power, Kato’s square root problem

Gurevich Pavel, Väth Martin: Stability for Semilinear Parabolic Problems in $L_2$ and $W^{1,2}$. Z. Anal. Anwend. 35 (2016), 333-357. doi: 10.4171/ZAA/1568