Renormalized entropy solutions of scalar conservation laws with boundary condition
| dc.contributor.author | Carrillo Menéndez, José | |
| dc.contributor.author | Wittbold, Petra | |
| dc.date.accessioned | 2023-06-20T16:53:26Z | |
| dc.date.available | 2023-06-20T16:53:26Z | |
| dc.date.issued | 2002-10 | |
| dc.description.abstract | We study an initial boundary value problem for a scalar conservation law u(t) + div Phi(u) = f on a bounded domain. Existence and uniqueness of a renormalized entropy solution is established for general L-1-data, Phi is an element ofC(R, R-N | |
| 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/15576 | |
| dc.identifier.doi | 10.1006/jdeq.2002.4179 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022039602941793 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57343 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of differential equations | |
| dc.language.iso | eng | |
| dc.page.final | 160 | |
| dc.page.initial | 137 | |
| dc.publisher | Elsevier Science | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | conservation law | |
| dc.subject.keyword | boundary condition | |
| dc.subject.keyword | L1-theory | |
| dc.subject.keyword | renormalized entropy solution | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Renormalized entropy solutions of scalar conservation laws with boundary condition | |
| dc.type | journal article | |
| dc.volume.number | 185 | |
| dcterms.references | C. Bardos, A. Y. Leroux, and J. C. Nedelec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979), 1017–1034. 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. 22 (1995), 241–273. Ph. Be´nilan, A. Pazy, and M. G. Crandall, ‘‘Nonlinear Evolution Equations in Banach Spaces,’’ to appear. Ph. Be´nilan, J. Carrillo, and P. Wittbold, Renormalized entropy solutions of scalar conservations laws, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000), 313–329. D. Blanchard and F. Murat, Renormalised solutions of nonlinear parabolic problems with L1-data: existence and uniqueness, Proc. Roy. Soc. Edinburgh 127A (1997), 1137-1152. D. Blanchard and H. Redwane, Solutions re´normalise´es d’e´quations paraboliques a` deux nonline´ arite´ s, C.R. Acad. Sci. 319 (1994), 831–835. J. Carrillo, Entropy solutions of nonlinear degenerate problems, Arch. Rational Mech. Anal. 147 (1999), 269–361. J. Carrillo, Conservation laws with discontinuous flux functions and boundary conditions, J. Evol. Equations, in press. J. Carrillo and P. Wittbold, Uniqueness of renormalized solutions of degenerate elliptic parabolic problems, J. Differential Equations 156 (1999), 93–121. J. Carrillo and P. Wittbold, Renormalized entropy solutions of nonlinear degenerate problems, in preparation. J. Carrillo and P. Wittbold, Conservation laws with general boundary conditions, in preparation. G. Dal Maso, F. Murat, L. Orsina, and A. Prignet, Renormalized solutions of elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999), 741–809. R. DiPerna, Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal. 88 (1985), 223–270. R. J. DiPerna and P. L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. 130 (1989), 321–366. S. N. Kruzhkov, Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations, Soviet Math. Dokl. 10 (1969), 785–788. S. N. Kruzhkov, First-order quasilinear equations in several independent variables, Math. USSR-Sb. 10 (1970), 217–243. F. Murat, Soluciones renormalizadas de EDP elipticas no lineales, Publ. Laboratoire d’Analyse Nume´rique, Univ. Paris 6, R 93023, 1993. RENORMALIZED ENTROPY SOLUTIONS 159 F. Otto, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Se´r. I 322 (1996), 729–734. A. Szepessy, Measure-valued solutions of scalar conservation laws with boundary conditions, Arch. Rational Mech. Anal. 107 (1989), 182–193. G. Vallet, Dirichlet problem for a nonlinear conservation law, Rev. Mat. Compl. XIII (2000), 231–250. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 48ac980d-beb1-40b0-acec-caec3a109b1c | |
| relation.isAuthorOfPublication.latestForDiscovery | 48ac980d-beb1-40b0-acec-caec3a109b1c |
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