Nonlocal elliptic-parabolic equation arising in the transient regime of a magnetically confined plasma in a Stellarator
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Lerena, Belén | |
| dc.contributor.author | Padial Molina, Juan Francisco | |
| dc.contributor.author | Rakotoson, Jean Michel Theresien | |
| dc.date.accessioned | 2023-06-20T16:53:31Z | |
| dc.date.available | 2023-06-20T16:53:31Z | |
| dc.date.issued | 1999 | |
| dc.description.abstract | We prove the existence and the regularity of solutions of an elliptic-parabolic equation involving the notions of relative rearrangement and monotone rearrangement. These equations were obtained from 3D MHD systems, taking, (in particular) into account the Ohm and Faraday's laws and the averaging arguments of Hender and Carreras for obtaining a 2D evolution model. Due to the presence of a strong nonlinearity, we introduce a new notion of solution derived from a new property of the relative rearrangement. This allows us to improve the results obtained in the stationnary case by cancelling the condition of smallness of the parameter lambda in the pressure. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15584 | |
| dc.identifier.doi | 10.1016/S0764-4442(99)90005-8 | |
| dc.identifier.issn | 0764-4442 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0764444299900058 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57347 | |
| dc.issue.number | 9 | |
| dc.journal.title | Comptes Rendus de l'Académie des Sciences. Série I. Mathématique | |
| dc.language.iso | eng | |
| dc.page.final | 777 | |
| dc.page.initial | 773 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.928 | |
| dc.subject.keyword | relative rearrangement | |
| dc.subject.keyword | monotone rearrangement | |
| dc.subject.keyword | 3D MHD systems | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Nonlocal elliptic-parabolic equation arising in the transient regime of a magnetically confined plasma in a Stellarator | |
| dc.type | journal article | |
| dc.volume.number | 329 | |
| dcterms.references | Almgrem F.J., Lieb E., J. Amer. Math. Sot. 2 (1989) 683-772. Ah H.W., Luckhaus S., Quasilinear elliptic-parabolic differential equations of parabolic type, Math. Z. 183 (1983) 31 I-341. Bear J., Dynamics of fluids in porous media, American Elzevier Publishing Company Inc., New York, 1972. Diaz J.I., Lerena B., Padial J.F., Rakotoson J.-M., (en preparation). Dfaz J.I., Padial J.F., Rakotoson J.-M., Nonlin. Anal. Th. Meth. and Appl. 34 (1998) 857-887. Dfaz J.I., Rakotoson J.-M., Arch. Rational Mech. and Anal. 134 (1996) 53-95. Hender T.C., Carreras B.A., Equilibrium calculation for helical axis Stellarators, Phys. Fluids 27 (1984) 2101-2120. Mossino J., Inégalites isoperimétriques, Collection “Travaux en cot&‘, Herman, Paris, 1984. Mossino J.,Rakotoson J.-M., Annalli della Scu. Norm. Sup. de Pisa XIII Serie IV (1) (1986). Mossino J., Temam R., Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in Plasma physics, Duke Math. J. 48 (1981) 475-495. Nelson D.B., Grad H., Heating and transport in Tokamaks of arbitrary shape and beta, Oak Ridge Report ORNUTM-6094,1978. Rakotoson J.-M., Differ. Integ. Eq. 12 (1) (1999) 67-81. Rakotoson J.-M., Temam R., Arch. Rational Mech. and Anal. 109 (1991) 213-238. Talenti G., Rearrangement and P.D.E., in: Inequalities fifty Years from Hardy, W.N. Event (Ed.), Marcel Dekker Inc., 1991, pp. 211-230. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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