Brandt, Felix ; Hieber, Matthias (2024)
Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem.
In: Bulletin of the London Mathematical Society, 2023, 55 (4)
doi: 10.26083/tuprints-00024693
Article, Secondary publication, Publisher's Version
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| Item Type: | Article |
|---|---|
| Type of entry: | Secondary publication |
| Title: | Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem |
| Language: | English |
| Date: | 9 February 2024 |
| Place of Publication: | Darmstadt |
| Year of primary publication: | 2023 |
| Place of primary publication: | Hoboken |
| Publisher: | Wiley |
| Journal or Publication Title: | Bulletin of the London Mathematical Society |
| Volume of the journal: | 55 |
| Issue Number: | 4 |
| DOI: | 10.26083/tuprints-00024693 |
| Corresponding Links: | |
| Origin: | Secondary publication DeepGreen |
| 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. |
| Status: | Publisher's Version |
| URN: | urn:nbn:de:tuda-tuprints-246937 |
| Additional Information: | MSC 2020: 35B10, 35K59, 92C17, 35Q92 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics > Analysis 04 Department of Mathematics > Analysis > Angewandte Analysis |
| Date Deposited: | 09 Feb 2024 13:35 |
| Last Modified: | 17 Apr 2024 06:39 |
| SWORD Depositor: | Deep Green |
| URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/24693 |
| PPN: | 517169789 |
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