On the uniqueness of solutions of a nonlinear elliptic problem arising in the confinement of a plasma in a stellarator device
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Galiano, Gonzalo | |
| dc.contributor.author | Padial Molina, Juan Francisco | |
| dc.date.accessioned | 2023-06-20T16:54:08Z | |
| dc.date.available | 2023-06-20T16:54:08Z | |
| dc.date.issued | 1999 | |
| dc.description.abstract | We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions, The inverse problem arises in the modeling of the magnetic confinement of a plasma in a Stellarator device. The uniqueness proof relies on an L-infinity-estimate on the solution of an auxiliary nonlocal problem formulated in terms of the relative rearrangement of a datum with respect to the solution. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CIEMAT=EURATOM association. | |
| dc.description.sponsorship | DGES (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15676 | |
| dc.identifier.doi | 10.1007/s002459900098 | |
| dc.identifier.issn | 0095-4616 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/txbb9g2vdymjc6m9/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57378 | |
| dc.issue.number | 1 | |
| dc.journal.title | Applied mathematics and optimization | |
| dc.language.iso | eng | |
| dc.page.final | 73 | |
| dc.page.initial | 61 | |
| dc.publisher | Springer | |
| dc.relation.projectID | 72=93 | |
| dc.relation.projectID | PB96-0583 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.97 | |
| dc.subject.keyword | free-boundary problem | |
| dc.subject.keyword | rearrangement | |
| dc.subject.keyword | equilibrium | |
| dc.subject.keyword | uniqueness of solution | |
| dc.subject.keyword | nonlinear elliptic equations | |
| dc.subject.keyword | nonlinear equations | |
| dc.subject.keyword | relative rearrangement | |
| dc.subject.keyword | plasma physics | |
| dc.subject.ucm | Análisis numérico | |
| dc.subject.unesco | 1206 Análisis Numérico | |
| dc.title | On the uniqueness of solutions of a nonlinear elliptic problem arising in the confinement of a plasma in a stellarator device | |
| dc.type | journal article | |
| dc.volume.number | 39 | |
| dcterms.references | Berestycki H, Brezis H (1980) On a free boundary problem arising in plasma physics. Nonlinear Anal 4:415–436 Blum J (1989) Numerical Simulation and Optimal Control in Plasma Physics. Gauthier Vilars, Paris Boozer AH (1982) Establishment of magnetic coordinates for a given magnetic field. Phys Fluids 25:520 Díaz JI (1992) Modelos bidimensionales de equilibrio magnetohidrodin´amico para Stellarators: Informe # 1. Association EURATOM-CIEMAT, Madrid Díaz JI (1993) Modelos bidimensionales de equilibrio magnetohidrodin´amico para Stellarators: Informe # 2. Association EURATOM-CIEMAT, Madrid Díaz JI, Padial JF, Rakotoson JM (1998) Mathematical treatment of the magnetic confinement in a current carrying Stellarator. Nonlinear Anal TMA 34:857–887 Díaz JI, Rakotoson JM (1993) On a two–dimensional stationary free boundary problem arising in the confinement of a plasma in a Stellarator. CR Acad Sci Paris Ser I 317:353–358 Díaz JI, Rakotoson JM (1996) On a nonlocal stationary free boundary problem arising in the confinement of a plasma in a Stellarator geometry. Arch Rational Mech Anal 134:53–95 Hender TC, Carreras BA (1984) Equilibrium calculations for helical axis Stellarators. Phys Fluids 27:2101–2109 Hernández J (1986) Qualitative methods for nonlinear diffusion equations. In Nonlinear Diffusion Problems (A. Fasano and M. Primicerio eds). Lecture Notes in Mathematics 1224. Springer-Verlag. Berlin, pp 47–118 Mossino J (1995) On some nonlocal models for the equilibrium of a confined plasma. In Modelos Matemáticos en Física de Plasmas (J.I. Díaz and A. Galindo eds). Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie de Ciencias Exactas. Tomo XXX. Madrid, pp 145–156 Mossino J, Temam R (1981) Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in plasma physics. Duke Math J 48:475–495 Puel P (1977) Sur un problème de valeur propre non linearie et de frontière libre. CR Acad Sci Paris Ser I 284:861–863 Rakotoson JM (1988) Some properties of the relative rearrangement. J Math Anal Appl 135:475–495 Rakotoson JM (1995) Relative rearrangement for highly nonlinear equations. Nonlinear Anal TMA 24(4):493–507 Schaeffer DG (1977) Nonuniqueness in the equilibrium shape of a confined plasma. Comm Partial Differential Equations 2(6):587–600 Temam R (1975) A nonlinear eigenvalue problem: equilibrium shape of a confined plasma. Arch Rational Mech Anal 60:51–73 Temam R (1977) Remarks on a free boundary value problem arising in plasma physics. Comm Partial Differential Equations 2:563–585 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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