Space and time localization in the flow of 2 immiscible fluids through a porous-medium - energy methods applied to systems
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Antontsev, S.N. | |
| dc.date.accessioned | 2023-06-20T16:57:32Z | |
| dc.date.available | 2023-06-20T16:57:32Z | |
| dc.date.issued | 1991-02 | |
| dc.description.abstract | Since the beginnings of the 1980s some energy methods have been introduced as an alternative to comparison principles in order to prove space and time localization of solutions of suitable nonlinear parabolic or elliptic equations. The study of nonhomogeneous equations (i.e. with prescribed right-hand terms) was considered by the authors [(*) Recent advances in nonlinear elliptic and parabolic problems, Proc. Int. Conf., Nancy/France 1988, Pitman Res. Notes Math. Ser. 208, 3-14 (1989; Zbl 0696.35090), and Dokl. Akad. Nauk SSSR 303, No.3, 524-529 (1988; Zbl 0684.35025)] proving new results on the retention of the free boundary (separating the region of the domain where the solution vanishes). In this work we wish to explain how to extend the results obtained in (*) for scalar equations to the case of systems of equations (even of different types). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CICYT (Spain). | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16283 | |
| dc.identifier.doi | 10.1016/0362-546X(91)90032-V | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/0362546X9190032V | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57514 | |
| dc.issue.number | 4 | |
| dc.journal.title | Nonlinear Analysis: Theory, Methods & Applications | |
| dc.language.iso | eng | |
| dc.page.final | 313 | |
| dc.page.initial | 299 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PBS6-04S5 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.55 | |
| dc.subject.cdu | 517.95 | |
| dc.subject.keyword | energy methods | |
| dc.subject.keyword | 2-phase flows in porous media | |
| dc.subject.keyword | space and time localization properties | |
| dc.subject.keyword | equations | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Space and time localization in the flow of 2 immiscible fluids through a porous-medium - energy methods applied to systems | |
| dc.type | journal article | |
| dc.volume.number | 16 | |
| dcterms.references | ALT H. W. & Dr BENEDETTO L., Nonsteady flow of water and oil through inhomogeneous poraus media, preprint No. 614, University of Bonn (19S3). ALT H. W. & LUCKHAUS S., Quasilinear elliptic-parabolic differential equations, Matiz. Z. 183,311-341 (1983. ANTONTSEV S. N., Finite speed of propagation of disturbances in multidimensional two-phase filtration problems.Zapiski Nauchn. Seminar. LOMI A.N.SSSR 96,3-12(1980) (in Russian). ANTONTSEV S.N.,Localization of solutions of degenerate equations in continuum mechanics. Institute of Hydrodynamics. S.O.A.N. SSSR (1986) (in Russian). ANTONTSEV S.N.& DíAZ J.I.,New results on localization of solutions of nonlinear elliptic or parabolic equations via energy methods, Dokl.Acad.Nauk.URSS Matiz.303,524-528(1988). ANTONTSEV S.N.& DÍAZ J. I., Applications of energy methods for localization of solutions of equations in continuum mechanics, Dokl. Acad. Nauk. URSS Math. 303, 320-326 (1988). ANTONTSEV S.N.& DíAZ J.I.,On space or time localization of solutions of non linear elliptic or parabolic equations via energy methods, in Recent advances in Nonlinear Elliptic and Parabolic Problems (Edited by P. BENILAN et al.),Pitman Research Notes in Mathematics,No.208,3-14. Longman, London (1989). ANTONTSEV S.N.&DíAZ J.I.,Energy methods and localization of solutions for continuum mechanics equations,J. appl. Mech. Tech. Phys. 2, 18-25 (1989). ANTONTSEV S. N.,KAZHIKHOV A.V.& MONAKHOV V.N., Boundary Value Problems in Mechanics of Inhomogeneous Fluids. Nauka, Novosibirsk (1983)(in Russian). BAMBERGER A.,Etude d'une équation doub1ement non Lineaire, J. funct. Analysis 24, 148-155 (1977). BEAR J.,Dynamics of Fluids in Porous Media. Elsevier, New York (1971). CHAVENT G. & JAFFRE J.,Mathematical Models and Finite Elements for Reservoir Simulation.North-Holland,Amsterdam (1986). DíAZ J.I.& VERON L.,Local vanishing properties of solutions of elliptic and parabolic equations, Trans. Am.Math. Soc. 290, 787-814 (1985). GAGNEUX O.,Une approche analytique nouvelle des modéles de la récuperation secondée en ingéniérie pétroliére,J. Mecanique theorique appliquée 5, 3-20 (1986). KRUZKOV S.N. & SUKORJANSKI S.M.,Boundary value problems for systems of equations of two phase porous flow type: statement of the problems, questions of solvability, justification of approximate methods, Math.Sbornik 33,62-80 (1977). NIRENBERG L., An extended interpolation inequality, Annali. Scu. norm. Sup. Pisa 20,733-737 (1966). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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