Asymptotic behaviour of time-dependent Ginzburg-Landau equations of superconductivity
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Wang, Bixiang | |
| dc.contributor.author | Willie, Robert | |
| dc.date.accessioned | 2023-06-20T17:10:53Z | |
| dc.date.available | 2023-06-20T17:10:53Z | |
| dc.date.issued | 1999-12 | |
| dc.description.abstract | In this paper, we establish the global fast dynamics for the time-dependent Ginzburg-Landau equations of superconductivity. We show the squeezing property and the existence of finite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in L-2 x L-2 for the Ginzburg-Landau equations in two spatial dimensions. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES | |
| dc.description.sponsorship | Ministerio de Educacion y Cultura (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19906 | |
| dc.identifier.doi | 10.1002/(SICI)1099-1476(199912)22:18<1647::AID-MMA97>3.0.CO;2-W | |
| dc.identifier.issn | 0170-4214 | |
| dc.identifier.officialurl | http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1099-1476(199912)22:18%3C1647::AID-MMA97%3E3.0.CO;2-W/pdf | |
| dc.identifier.relatedurl | http://onlinelibrary.wiley.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57902 | |
| dc.issue.number | 18 | |
| dc.journal.title | Mathematical Methods in the Applied Sciences | |
| dc.language.iso | eng | |
| dc.page.final | 1669 | |
| dc.page.initial | 1647 | |
| dc.publisher | W. Spröβig | |
| dc.relation.projectID | PB96-0648 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Global attractor | |
| dc.subject.keyword | Ginzburg-Landau equations | |
| dc.subject.keyword | Superconductivity | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Asymptotic behaviour of time-dependent Ginzburg-Landau equations of superconductivity | |
| dc.type | journal article | |
| dc.volume.number | 22 | |
| dcterms.references | Adams, R. A., Sobolev Spaces, Academic Press, New York, 1975. Chen, Z. M., Hoffmann, K. H. and Liang, J., ‘On a non-stationary Ginzburg–Landau superconductivity model’, Math. Meth. in the Appl. Sci., 16, 855–875 (1993). Du, Q., ‘Global existence and uniqueness of solutions of the time-dependent Ginzburg–Landau model for superconductivity’, Appl. Anal., 53, 1–17 (1994). Eden, A., Foias, C., Nicolaenko, B. and Temam, R., ‘Ensembles inertiels pour des equations devolution dissipatives’, C.R. Acad. Sci. Paris, 310, 559–562 (1990). Fleckinger-Pellé, J. and Kaper, H. G., ‘Gauges for the Ginzburg–Landau equations of superconductivity, Proc. ICIAM '95’, Z. Angew. Math. Mech., 76, 345–348 (1996). Fleckinger-Pellé, J., Kaper, H. G. and Takáč, P., ‘Dynamics of the Ginzburg–Landau equations of superconductivity’, Nonl. Anal. TMA, 32, 647–665 (1998). Girault, V. and Raviart, P., Finite Element Methods for Navier–Stokes Equations, Springer, New York, 1986. Gor'kov, L. P. and Eliashberg, G. M., ‘Generalizations of the Ginzburg–Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities’, Zh. Eksp. Teor. Fiz., 54, 612–626 (1968). Sov. Phys. JETP, 27, 328–334 (1968). Henry, D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer, New York, 1981. Kaper, H. G. and Takáč, P., ‘Ginzburg–Landau dynamics with a time dependent magnetic field’, Nonlinearity, 11, 291–305 (1998). Kaper, H. G., Wang, B. and Wang, S., ‘Determining nodes for the Ginzburg–Landau equations of superconductivity’, Discrete Continuous Dyn. Systems, 4, 205–224 (1998). Liang, J. and Tang, Q., ‘Asymptotic behaviour of an evolutionary Ginzburg–Landau superconductivity model’, J. Math. Annal. Appl., 195, 92–107 (1995). Schmid, A., ‘A time dependent Ginzburg–Landau equation and its application to the problem of resistivity in the mixed state’, Phys. Kondens. Mater. 5, 302–317 (1996). Takáč, P., ‘On the dynamical process generated by a superconductivity model’, Proc. ICIAM'95, Z. Angew. Math. Mech., 76, 349–352 (1996). Tang, Q., ‘On an evolutionary system of Ginzburg–Landau equations with fixed total magnetic flux’, Commun. Partial Differential Equation 20, 1–36 (1995). Tang, Q. and Wang, S., ‘Time dependent Ginzburg–Landau equations of superconductivity’, Physica D, 88, 139–166 (1995). Temam, R., Infintie Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1998 Tinkham, M., Introduction to Superconductivity, 2nd edn., McGraw-Hill, New York, 1996. Wang, B. and Wang, S., ‘Gevrey class regularity for the solutions of the Ginzburg–Landau equations of superconductivity’, Discrete Continuous Dyn. Systems 4, 507–522 (1998). Wang, S. and Zhan, M., Lp &Solutions to the time-dependent Ginzburg-Landau equations of superconductivity, preprint, 1996 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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