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
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Brandt, Felix ; Hieber, Matthias |
| Art des Eintrags: | Bibliographie |
| Titel: | Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem |
| Sprache: | Englisch |
| Publikationsjahr: | 2023 |
| Ort: | Hoboken |
| Verlag: | Wiley |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Bulletin of the London Mathematical Society |
| Jahrgang/Volume einer Zeitschrift: | 55 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1112/blms.12831 |
| Zugehörige Links: | |
| Kurzbeschreibung (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. |
| Zusätzliche Informationen: | MSC 2020: 35B10, 35K59, 92C17, 35Q92 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis 04 Fachbereich Mathematik > Analysis > Angewandte Analysis |
| Hinterlegungsdatum: | 13 Feb 2024 15:01 |
| Letzte Änderung: | 07 Mär 2024 14:54 |
| PPN: | 516076957 |
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| Suche nach Titel in: | TUfind oder in Google |
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Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem. (deposited 09 Feb 2024 13:35)
- Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem. (deposited 13 Feb 2024 15:01) [Gegenwärtig angezeigt]
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