On a nonlocal elliptic problem arising in the magnetic confinement of a plasma in a Stellarator
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.date.accessioned | 2023-06-20T16:54:28Z | |
| dc.date.available | 2023-06-20T16:54:28Z | |
| dc.date.issued | 1997-12 | |
| dc.description | 2nd World Congress on Nonlinear Analysts.ATHENS, GREECE.JUL 10-17, 1997 | |
| dc.description.abstract | This paper is a review of recent results (including the author's work) on a two-dimensional free-boundary problem, modeling magnetohydrodynamic equilibrium in a stellarator nuclear fusion device. The main tools used in the paper under review are decreasing rearrangement (applied to the magnetic flux) and relative rearrangement (with respect to the magnetic flux) | |
| 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/15730 | |
| dc.identifier.doi | 10.1016/S0362-546X(97)00269-1 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0362546X97002691 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57392 | |
| dc.issue.number | 7 | |
| dc.journal.title | Nonlinear Analysis: Theory, Methods and Applications | |
| dc.language.iso | eng | |
| dc.page.final | 3974 | |
| dc.page.initial | 3963 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.97 | |
| dc.subject.keyword | nonlocal nonlinear elliptic problem | |
| dc.subject.keyword | plasma physics | |
| dc.subject.keyword | Stellarator devices | |
| dc.subject.keyword | decreasing and relative rearrangements | |
| dc.subject.keyword | Galerkin method | |
| dc.subject.keyword | free boundary problem | |
| dc.subject.keyword | free-boundary problem | |
| dc.subject.keyword | equilibrium | |
| dc.subject.keyword | rearrangement | |
| dc.subject.keyword | equation. | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | On a nonlocal elliptic problem arising in the magnetic confinement of a plasma in a Stellarator | |
| dc.type | journal article | |
| dc.volume.number | 30 | |
| dcterms.references | F.J. Almagren, E. Lieb. Symmetric decreasing rearrangement is sometimes continuous, J. Am. Math. Soc., 2 (1989), pp. 683–772 E. Beretta, M. Vogehus. An inverse problem originating from Magnetohydrodynam- ics II: the case of the Grad-Shafranov Equation Indiana University Mathematics Journal, 41 (4) (1992), pp. 1081–1117 H. Berstycki, H. Brezis. On a free boundary problem arising in plasma physics. Nonlinear Anal, 4 (1980), pp. 415–436 A. Bermudez, M.L. Seoane. Desarrollo de un codigo de equilibrio usando métodos de elementos finitos CIEMAT/EURATOM Association Reports (1996) J. Blum. Numerical simulation and optimal control in Plasma Physics Wiley, Gauthier-Villars (1989) A.H. Boozer. Establishment of magnetic coordinates for given magnetic field. Phys. Fluids, 25 (1982), pp. 520–521 W.A. Cooper. Global external ideal magnetohydrodynamic instabilities in three- dimensional plasmas Proc. of the Joint Varenna-Laussane, Workshop, Theory of Fusion Plasmas, Edit. Compositori, Paris (1990) J.I. Díaz. Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. 1993 Informe 1, 2 and 3. CIEMAT/EURATOM Association Reports (1992) J.I. Diaz. Un problema de frontera libre en el estudio del equilibrio magnetohidrodinámico de un plasma en una configuratión Stellarator Madrid ,in: J.I. Díaz, A. Galindo (Eds.), The book Modelos Matemáticos en Física de Plasmas, Memorias de la Real Academia de Ciencias ExactasFisicas y Naturales. Serie de Ciencias Exactas, Tomo XXX (1995), pp. 73–132 Diaz J.I., Galiano G. and Padial J.F., On the uniqueness of solutions of a nonlinear elliptic problem arising in the confinement of a plasma in a Stellarator device, To appear. Diaz J.I., Padial J.F. and Rakotoson J.M., Mathematical treatment of the magnetic confinement in a current carrying Stellarator, To appear. J.I. Díaz, J.M. Rakotoson. On a two-dimensional stationary free boundary problem arising in the confinement of a plasma in a Stellarator. Série I C.R. Acad. Sci. Paris, 317 (1993), pp. 353–358 J.I. Díaz, J.M. Rakotoson. On a nonlocal stationary free boundary problem arising in the confinement of a plasma in a Stellarator geometry. Arch. Rational Mech. Anal., 134 (1996), pp. 53–95 J.P. Freidberg. Ideal Magnetohydrodynamics. Plenum Press, Bologna (1987) A. Friedman. Variational principles and free-boundary problems, John Wiley and Sons, New York (1982) H. Grad, P.N. Hu, D.C. Stevens. Adiabatic evolution of plasma equilibrium. Proc. Nat. Acad. Sci. USA, 72 (1975), pp. 3789–3793 J.M. Greene, J.L. Johnson. Determination of Hydromagnetic Equilibria. Phys. Fluids, 4 (1961) T.C. Hender, B.A. Carreras. Equilibrium calculations for helical axis Stellarators. Phys. Fluids, 27 (1984), p. 2101 J.L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires Dunod, Gauthier-Villars, New York (1969) J. Mossino. Inégalités isoperimetriques et applications en physique. Hermann, Paris (1984) J. Mossino. On some Nonlocal Models for the Equilibrium of a Confined Plasma Madrid ,in: J.I. Diaz, A. Galindo (Eds.), The book Modelos Matemáticos en Fisica de Plasmas, Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie de Ciencias Exactas, Tomo XXX (1995), pp. 145–156 J. Mossino, J.M. Rakotoson. Isoperimetric inequalities in parabolic equations. Série IV Annali della Scuola Normale Superiore di Pisa, Vol. XIII (1986), pp. 51–73. J. Mossino, R. Temam. Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in Plasma Physics. Duke Math. J., 48 (1981), pp. 475–495 J.F. Padial, J.M. Rakotoson, L. Tello. Introduction to monotone and relative rearrangements and applications. Département de Mathématiques. Univ. de Poitiers, report No. 81 (1993) P. Puel. Sur un problème de valeur propre non linearie et de frontière libre. CRAS, 284 (1977), pp. 861–863 J.M. Rakotoson. Some properties of the relative rearrangement. J. Math. Anal. Appl., 135 (1988), pp. 475–495 J.M. Rakotoson. Differentiability of the relative rearrangement. Diff. and Int. Equation, 2 (1989), pp. 363–377 J.M. Rakotoson. Relative rearrangement for hilghly non linear equations. Nonlinear Analysis, Theory, Meth. and Appl., 24 (1995), pp. 493–507 J.M. Rakotoson. Strong continuity of the relative rearrangement maps and application to a Galerkin approach for nonlocal problems. App. Math. Lett., 8 (1995), pp. 61–63 Rakotoson J.M., Galerkin approximation, strong continuity of the relative rearrangement maps and application to plasma physics equations. To appear. DG Schaeffer. Non uniqueness in the equilibrium shape of a confined plasma Comm in Partial Differential Equations, 2 (1977), pp. 587–600 J. Simon. Asymptotic behaviour of a plasma induced by an electric current. Nonlinear Analysis (1985), pp. 149–169 G. Talenti. Elliptic equations and rearrangements. série IV Annali della Scuola Norm. Sup. di Pisa, 4 (1976), pp. 697–718 R. Temam. A nonlinear eigenvalue problem: equilibrium shape of a confined plasma. Arch. Rational Mec. Anal, 60 (1975), pp. 51–73 R. Temam. Remarks on a free boundary problem arising in Plasma Physics. Comm. in Partial Diff. Equations, 2 (1977), pp. 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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