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Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

Bruell, Gabriele

Abstract. The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap.
Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.

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Volltext §
DOI: 10.5445/IR/1000096410
Veröffentlicht am 12.07.2019
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2019
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000096410
Verlag KIT, Karlsruhe
Umfang 14 S.
Serie CRC 1173 ; 2019/12
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Bemerkung zur Veröffentlichung SFB/1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)

SFB 1173: Wellenphänomene: Analysis und Numerik. (1. Förderperiode)
Schlagwörter local well-posedness, thin film equations, degenerate parabolic system, mixed orders, asymptotic stability
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