Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
| dc.contributor.author | Carrillo Menéndez, José | |
| dc.contributor.author | Wittbold, Petra | |
| dc.date.accessioned | 2023-06-20T16:53:27Z | |
| dc.date.available | 2023-06-20T16:53:27Z | |
| dc.date.issued | 1999-07 | |
| dc.description.abstract | We consider a general class of degenerate elliptic-paraboic problems associated with the equation b(v)(t) = div a(v, Dv) + f. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in L-1 for renormalized solutions | |
| 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 | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15577 | |
| dc.identifier.doi | 10.1006/jdeq.1998.3597 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022039698935975 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57344 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Differential Equations | |
| dc.language.iso | eng | |
| dc.page.final | 121 | |
| dc.page.initial | 93 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PB93-0434 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Equations of mixed type | |
| dc.subject.keyword | Degenerate elliptic equations | |
| dc.subject.keyword | Degenerate parabolic equations | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems | |
| dc.type | journal article | |
| dc.volume.number | 156 | |
| dcterms.references | H. W. Alt and S. Luckhaus, Quasi-linear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311 341. S. J. Alvarez and J. Carrillo, A free boundary problem in theory of lubrication, Comm. Partial Differential Equations 19 (1994), 1743 1761. Ph. Be nilan, L. Boccardo, Th. Galloue t, R. Gariepy, M. Pierre, and J.-L. Vazquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), 241 273. Ph. Be nilan and P. Wittbold, On mild and weak solutions of elliptic-parabolic problems, Adv. Differential Equations 1 (1996), 1053 1073. Ph. Be nilan and P. Wittbold, Sur un proble me parabolique elliptique, M2AN, to appear. D. Blanchard and F. Murat, Renormalised solutions of nonlinear parabolic problems with L1 data: Existence and uniqueness, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 1137 1152. D. Blanchard and H. Redwane, Solutions re normalise es d'e quations paraboliques a deux non line arite s, C.R. Acad. Sci. Paris 319 (1994), 831 835. L. Boccardo, D. Giachetti, J. I. Diaz, and F. Murat, Existence of a solution for a weaker form of a nonlinear elliptic equation, in ``Recent Advances in Nonlinear Elliptic and Parabolic Problems,'' Pitman Research Notes in Mathematics Series, Vol. 208, pp. 229 246, Longman Sci. Tech., Harlow, 1989. J. Carrillo, Unicite des solutions du type Kruskov pour des proble mes elliptiques avec des termes de transport non line aires, C.R. Acad. Sci. Paris 303 (1986), 189 192. J. Carrillo, On the uniqueness of the solution of the evolution dam problem, Nonlinear Anal. 22 (1994), 573 607. J. Carrillo, Entropy solutions for nonlinear degenerate problems, submitted for publication. J. Carrillo and M. Chipot, On some nonlinear elliptic equations involving derivatives of the nonlinearity, Proc. Roy. Soc. Edinburgh 100 (1985), 281 294. A. Plouvier-Debaigt, B. Donne, G. Gagneux, and P. Urruty, Solutions re normalise es pour des mode les des milieux poreux, C.R. Acad. Sci. Paris Se r. I 325 (1997), 1091 1095. R. J. Di Perna and P. L. Lions, On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Ann. of Math. (2) 130 (1989), 321 366. G. Gagneux and M. Madaune-Tort, Unicite des solutions faibles d'e quations de diffusion convection, C.R. Acad. Sci. Paris 318 (1994), 919 924. G. Gagneux and M. Madaune-Tort, ``Analyse mathe matique de mode les non line aires de l'inge nierie pe trolie re,'' Mathe matiques et Applications, Vol. 22, Springer, Berlin, 1996. S. N. Kruzhkov, First-order quasilinear equations in several independent variables, Math. USSR Sb. 10 (1970), 217 243. F. Murat, ``Soluciones renormalizadas de EDP el@ pticas no lineales,'' Publ. Laboratoire d'Analyse Nume rique, Univ. Paris 6, 93023, 1993. F. Otto, L1-Contraction and uniqueness for quasilinear elliptic parabolic problems, J. Differential Equations 131 (1996), 827 848. J. M. Rakotoson, Generalized solutions in a new type of sets for problems with measures as data, Differential Integral Equations 6 (1993), 27 36. J. M. Rakotoson, Uniqueness of renormalized solutions in a T-set for the L1-data and the link between various formulations, Indiana Univ. Math. J. 43 (1994), 285 293. P. Wittbold, Renormalized solutions of quasilinear elliptic parabolic problems, in preparation. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 48ac980d-beb1-40b0-acec-caec3a109b1c | |
| relation.isAuthorOfPublication.latestForDiscovery | 48ac980d-beb1-40b0-acec-caec3a109b1c |
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