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Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem

Brandt, Felix ; Hieber, Matthias (2023)
Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem.
In: Bulletin of the London Mathematical Society, 55 (4)
doi: 10.1112/blms.12831
Article, Bibliographie

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Abstract

This article develops an approach to unique, strong periodic solutions to quasilinear evolution equations by means of the classical Da Prato–Grisvard theorem on maximal Lp‐regularity in real interpolation spaces. The method is used to show that quasilinear Keller–Segel systems admit a unique, strong T‐periodic solution in a neighborhood of 0 provided the external forces are T‐periodic and satisfy certain smallness conditions. A similar assertion applies to a Nernst–Planck–Poisson type system in electrochemistry. The proof for the quasilinear Keller–Segel systems relies also on a new mixed derivative theorem in real interpolation spaces, that is, Besov spaces, which is of independent interest.

Item Type: Article
Erschienen: 2023
Creators: Brandt, Felix ; Hieber, Matthias
Type of entry: Bibliographie
Title: Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem
Language: English
Date: 2023
Place of Publication: Hoboken
Publisher: Wiley
Journal or Publication Title: Bulletin of the London Mathematical Society
Volume of the journal: 55
Issue Number: 4
DOI: 10.1112/blms.12831
Corresponding Links:
Abstract:

This article develops an approach to unique, strong periodic solutions to quasilinear evolution equations by means of the classical Da Prato–Grisvard theorem on maximal Lp‐regularity in real interpolation spaces. The method is used to show that quasilinear Keller–Segel systems admit a unique, strong T‐periodic solution in a neighborhood of 0 provided the external forces are T‐periodic and satisfy certain smallness conditions. A similar assertion applies to a Nernst–Planck–Poisson type system in electrochemistry. The proof for the quasilinear Keller–Segel systems relies also on a new mixed derivative theorem in real interpolation spaces, that is, Besov spaces, which is of independent interest.

Additional Information:

MSC 2020: 35B10, 35K59, 92C17, 35Q92

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Analysis
04 Department of Mathematics > Analysis > Angewandte Analysis
Date Deposited: 13 Feb 2024 15:01
Last Modified: 07 Mar 2024 14:54
PPN: 516076957
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