Stability of the travelling wave 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 | |
| dc.contributor.author | LORENZI, Luca | |
| dc.date.accessioned | 2024-04-04T02:38:20Z | |
| dc.date.available | 2024-04-04T02:38:20Z | |
| dc.date.created | 2008-09 | |
| dc.date.issued | 2009-03 | |
| dc.identifier.issn | 1937-5093 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190868 | |
| dc.description.abstractEn | We investigate the stability of the travelling wave (TW) solution in a 2D Stefan problem, a simplified version of a solid-liquid interface model. It is intended as a paradigm problem to present our method based on: (i) definition of a suitable linear one dimensional operator, (ii) projection with respect to the $x$ coordinate only; (iii) Lyapunov-Schmidt method. The main issue is that we are able to derive a parabolic equation for the corrugated front $\varphi$ near the TW as a solvability condition. This equation involves two linear pseudo-differential operators, one acting on $\varphi$, the other on $(\varphi_y)^2$ and clearly appears as a generalization of the Kuramoto-Sivashinsky equation related to turbulence phenomena in chemistry and combustion. A large part of the paper is devoted to study the properties of these operators in the context of functional spaces in the $y$ and $x,y$ coordinates with periodic boundary conditions. Technical results are deferred to the appendices. | |
| dc.language.iso | en | |
| dc.publisher | AIMS | |
| dc.subject.en | Stefan problem | |
| dc.subject.en | stability | |
| dc.subject.en | front dynamics | |
| dc.subject.en | Kuramoto-Sivashinsky equation | |
| dc.subject.en | pseudo-differential operators | |
| dc.subject.en | sectorial operators | |
| dc.title.en | Stability of the travelling wave in a 2D weakly nonlinear Stefan problem | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Kinetic and Related Models | |
| bordeaux.page | 109-134 | |
| bordeaux.volume | 2 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00386986 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00386986v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Kinetic%20and%20Related%20Models&rft.date=2009-03&rft.volume=2&rft.issue=1&rft.spage=109-134&rft.epage=109-134&rft.eissn=1937-5093&rft.issn=1937-5093&rft.au=BRAUNER,%20Claude-Michel&HULSHOF,%20Josephus&LORENZI,%20Luca&rft.genre=article |
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