Stability for semilinear parabolic problems in \(L_2\) and \(W^{1,2}\) (Q330253)
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scientific article; zbMATH DE number 6643054
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability for semilinear parabolic problems in \(L_2\) and \(W^{1,2}\) |
scientific article; zbMATH DE number 6643054 |
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Stability for semilinear parabolic problems in \(L_2\) and \(W^{1,2}\) (English)
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25 October 2016
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Summary: 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.
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asymptotic stability
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existence
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uniqueness
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parabolic PDE
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strongly accretive operator
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sesquilinear form
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fractional power
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Kato's square root problem
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