Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRAUNER, Claude-Michel | |
| hal.structure.identifier | Department of Computer Science [Amsterdam] | |
| dc.contributor.author | HULSHOF, Josephus | |
| hal.structure.identifier | Dipartimento di Matematica | |
| dc.contributor.author | LORENZI, Luca | |
| dc.date.accessioned | 2024-04-04T02:34:49Z | |
| dc.date.available | 2024-04-04T02:34:49Z | |
| dc.date.created | 2009-07 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190579 | |
| dc.description.abstractEn | In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter $\varepsilon$ and define rescaled variables accordingly. At fixed $\varepsilon$, our method is based on: definition of a suitable linear 1D operator, projection with respect to the longitudinal coordinate only, Lyapunov-Schmidt method. As a solvability condition, we derive a self-consistent parabolic equation for the front. We prove that, starting from the same configuration, the latter remains close to the solution of K--S on a fixed time interval, uniformly in $\varepsilon$ sufficiently small. | |
| dc.language.iso | en | |
| dc.subject.en | pseudo-differential operators | |
| dc.subject.en | Kuramoto-Sivashinsky equation | |
| dc.subject.en | front dynamics | |
| dc.subject.en | Stefan problems | |
| dc.subject.en | singular perturbations | |
| dc.title.en | Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem. | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 0907.2758 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00404251 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00404251v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BRAUNER,%20Claude-Michel&HULSHOF,%20Josephus&LORENZI,%20Luca&rft.genre=preprint |
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