Existence of a traveling wave solution in a free interface problem with fractional order kinetics
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRAUNER, Claude-Michel | |
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| dc.contributor.author | ROUSSARIE, Robert | |
| hal.structure.identifier | Tongji University | |
| dc.contributor.author | SHANG, Peipei | |
| hal.structure.identifier | Tongji University | |
| dc.contributor.author | ZHANG, Linwan | |
| dc.date.accessioned | 2024-04-04T02:49:03Z | |
| dc.date.available | 2024-04-04T02:49:03Z | |
| dc.date.issued | 2021-04-25 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191790 | |
| dc.description.abstractEn | In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < α < 1. We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincaré-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is finite, meaning that the trailing interface is finite in contrast to the case α = 1, but in accordance with α = 0. Finally, the integro-differential system is solved via a fixed-point method. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Diffusional-thermal combustion | |
| dc.subject.en | Fractional order kinetics | |
| dc.subject.en | Free interface problems | |
| dc.subject.en | Traveling wave solutions | |
| dc.subject.en | Poincare-Bendixson Theorem | |
| dc.subject.en | Trapping triangles | |
| dc.title.en | Existence of a traveling wave solution in a free interface problem with fractional order kinetics | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jde.2021.01.034 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 2010.15685 | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.page | 105-147 | |
| bordeaux.volume | 281 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02979187 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02979187v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2021-04-25&rft.volume=281&rft.spage=105-147&rft.epage=105-147&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=BRAUNER,%20Claude-Michel&ROUSSARIE,%20Robert&SHANG,%20Peipei&ZHANG,%20Linwan&rft.genre=article |
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