Carrillo Menéndez, José
(2003)
*Conservation laws with discontinuous flux functions and boundary condition.*
Journal of evolution equations, 3
(2).
pp. 283-301.
ISSN 1424-3199

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## Abstract

In a bounded domain Omega we study the existence and uniqueness of entropy solutions of partial derivativeu/partial derivativet + div Phi(u) = f with u(0) = u(0), where Phi is allowed to have some discontinuities of first type.

Item Type: | Article |
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Uncontrolled Keywords: | Entropy solutions |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15575 |

References: |
Andreianov, B., Benilan, Ph. and Kruzhkov, S. N., L1 theory of scalar conservation law with continuous flux function. J. Funct. Anal. 171 (2000) no.1, 15–33. Bardos, C., Leroux, A. Y. and Nedelec, J. C., First order cuasilinear equations with boundary conditions. Comm. in P.D.E. 4 (1979), 1017–1034. Benilan, Ph., Equations d’´evolution dans un espace de Banach quelconque et applications. Th`ese d’´etat, Orsay 1972. Benilan, Ph., Carrillo, J. and Wittbold, P., Renormalized entropy solutions of scalar conservation laws. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000) no. 2, 313–327. Benilan, Ph. and Kruzhkov, S. N., Conservation laws with continuous flux functions. NoDEA Nonlinear Differential Equations Appl. 3 (1996) no.4, 395–419. Brezis, H., Op´erateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland 1973. Carrillo, J., Entropy solutions for nonlinear degenerate problems. Arch. Rational Mech. Anal. 147 (1999), 269–361. Carrillo, J. and Wittbold, P., Renormalized entropy solutions of scalar conservation laws with boundary condition. J. Diff. Eqs. 185 (2002), no. 1, 137–160. Crandall, M. G. and Ligget, T., Generation of semi-groups of nonlinear transformations in general Banach spaces. Amer. J. Math. 93 (1971), 265–298. Kruzhkov, S. N., Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order. Dokl. Akad. Nauk SSSR 187 (1969), 29–32, (English transl. in Soviet Math. Dokl. 10, (1969)). Kruzhkov, S. N., First order quasilinear equations in several independent variables. Math. Sbornik, 81 (1970), 228–255, (English transl. in Math. USSR Sb. 10, (1970)). Porretta, A. and Vovelle, J., L1 solutions to first order hyperbolic equations in bounded domains. To appear Otto, F., Initial boundary value problem for a scalar conservation law. C. R. Acad. Sci. Paris 322 S´erie I (1996) no.8, 729–734. Vallet, G., Dirichlet problem for a nonlinear conservation law. Rev. Mat. Complutense. 13 (2000) no.1, 231–250. |

Deposited On: | 11 Jun 2012 09:47 |

Last Modified: | 06 Feb 2014 10:27 |

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