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Ammar, Kaouther and Wittbold, Petra and Carrillo Menéndez, José
(2006)
*Scalar conservation laws with general boundary condition and continuous flux function.*
Journal of Differential Equations, 228
(1).
pp. 111-139.
ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S002203960600204X

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## Abstract

We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: u(t) + div Phi (u) = f on Q = (0, T) x Omega, u (0, (.))= u(0) on Q and "u = a on some part of the boundary (0, T) x partial derivative Omega." Existence and uniqueness of the entropy solution is established for any Phi is an element of C(R; R-N), u(0) is an element of L-infinity(Q), f is an element of L-infinity(Q), a is an element of L-infinity((0, T) x partial derivative Omega). In the L-1-setting, a corresponding result is proved for the more general notion of renormalised entropy solution.

Item Type: | Article |
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Uncontrolled Keywords: | Conservation law; Nonhomogeneous boundary conditions; Continuous flux; Penalization; L1-Theory;Renormalized entropy solution |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15555 |

Deposited On: | 11 Jun 2012 08:06 |

Last Modified: | 12 Dec 2018 15:07 |

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