On a quasilinear degenerate system arising in semiconductors theory. Part 1: Existence and uniqueness of solutions
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Galiano, Gonzalo | |
| dc.contributor.author | Jungel, Ansgar | |
| dc.date.accessioned | 2023-06-20T16:53:19Z | |
| dc.date.available | 2023-06-20T16:53:19Z | |
| dc.date.issued | 2001-09 | |
| dc.description.abstract | This paper is about the drift-diffusion equations for semiconductors. Existence and uniqueness of weak solutions are obtained. The existence is proved by using the regularization technique. The proof of the uniqueness is interesting. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15563 | |
| dc.identifier.doi | 10.1016/S0362-546X(00)00102-4 | |
| dc.identifier.issn | 1468-1218 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0362546X00001024 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57337 | |
| dc.issue.number | 3 | |
| dc.journal.title | Nonlinear Analysis: Real World Applications | |
| dc.language.iso | eng | |
| dc.page.final | 336 | |
| dc.page.initial | 305 | |
| dc.publisher | Pergamon Elsevier Science Ltd. | |
| dc.relation.projectID | PB96=0385. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 621.38 | |
| dc.subject.keyword | drift-diffusion model | |
| dc.subject.keyword | parabolic equations | |
| dc.subject.keyword | convection | |
| dc.subject.keyword | quasilinear degenerate system | |
| dc.subject.keyword | semiconductors | |
| dc.subject.ucm | Física matemática | |
| dc.title | On a quasilinear degenerate system arising in semiconductors theory. Part 1: Existence and uniqueness of solutions | |
| dc.type | journal article | |
| dc.volume.number | 2 | |
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Madaune-Tort, Unicitédes solutions faibles d’équations de diffusion-convection, C. R. Acad. Sci. t. 318, Ser. I (1994) 919–924. G. Gagneux, M. Madaune-Tort, Analyse mathématique de modèles non linéaires de l’ingeniérie pétrolière, Springer, Paris, 1996. G. Galiano, Sobre algunos problemas de la Mecáanica de Medios Continuos en los que se originan Fronteras Libres, Thesis, Universidad Complutense de Madrid, 1997. P. Grisvard, Elliptic Problems in Nonsmooth Domains,Pitman, Boston, 1985. A. Jüngel, On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci. 4 (1994) 677–703. A. Jüngel, Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci. 5 (1995) 497–518. A. Jüngel, Asymptotic analysis of a semiconductor model based on Fermi–Dirac statistics, Math.Methods Appl. Sci. 19 (1996) 401–424. A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, Math. Nachr. 185 (1997) 85–110. A.S. Kalashnikov, The Cauchy problem in a class of growing functions for equations of unsteady filtration type, Vestnik Moskov Univ. Ser. VI Mat. Mech. 6 (1963) 17–27. S.N. Kruzhkov, First order quasilinear equations in several independent variables, Math. USSR Sb. 10 (2) (1970) 217–243. S.N. Kruzhkov, S.M. Sukorjanski, Boundary value problems for systems of equations of two phase porous ffow type: statement of the problems, questions of solvability, justification of approximate methods, Math USSR Sb. 33 (1) (1977) 62–80. N.V. Krylov, Nonlinear elliptic and parabolic equations of the second order, D. Reidel Publishing Company, Dordrecht, 1987. O.A. Ladyzenskaya, V.A. Solonnikov, N.N. Ural’ceva, in: Quasilinear Equations of Parabolic Type,Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1968. J.L. Lions, Quelques méthodes de résolution des probl_emes aux limites non linéaires, Dunod, Gauthiers-Villars, Paris, 1969. P.A. Markowich, The Stationary Semiconductor Device Equations, Springer, Wien, 1986. P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer, Wien, 1990. M.S. Mock, On equations describing steady state carrier distributions in a semiconductor device, Comm.Pure Appl. Math. 25 (1972) 781–792. F. Otto, L1-contraction and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations 131 (1996) 20–38. J.F. Padial, A comparison principle for weak solutions of some nonlinear parabolic systems, preprint, 1997. W. Rudin, Real and Complex Analysis, 2nd Edition, McGraw-Hill, New York, 1974. J. Rulla, Weak solutions to Stefan Problems with prescribed convection, SIAM J. 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Sci. Norm. Sup.Pisa, Cl. Sci. IV 16 (1989) 165–224. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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