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Smooth extensions for
inertial manifolds of semilinear parabolic equations
Anna Kostianko and Sergey Zelik |
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Vol. 17 (2024), No. 2, 499–533
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Abstract |
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The paper is devoted to a comprehensive study of smoothness of inertial manifolds (IMs) for abstract semilinear parabolic problems. It is well known that in general we cannot expect more than -regularity for such manifolds (for some positive, but small ). Nevertheless, as shown in the paper, under natural assumptions, the obstacles to the existence of a -smooth inertial manifold (where is any given number) can be removed by increasing the dimension and by modifying properly the nonlinearity outside of the global attractor (or even outside the -smooth IM of a minimal dimension). The proof is strongly based on the Whitney extension theorem. |
Keywords
inertial manifolds, finite-dimensional reduction,
smoothness, Whitney extension theorem
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Mathematical Subject Classification
Primary: 35B40, 35B42, 37D10, 37L25
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Milestones
Received: 20 June 2021
Accepted: 26 July 2022
Published: 6 March 2024
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Authors |
| Anna Kostianko | ||
| Department of Mathematics Zhejiang Normal University Zhejiang China |
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| Sergey Zelik | ||
| Department of Mathematics Zhejiang Normal University Zhejiang China |
Department of Mathematics University of Surrey Guildford United Kingdom |
Keldysh Institute of Applied
Mathematics Moscow Russia |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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