Bénilan, Philippe and Carrillo Menéndez, José and Wittbold, Petra
(2002)
*Renormalized entropy solutions of scalar conservation laws.*
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV, 29
(2).
pp. 313-327.
ISSN 0391-173X

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## Abstract

A scalar conservation law ut +div (u) = f is considered with the initial datum u|t=0 = u0 2 L1 loc(RN) and f 2 L1

loc(RN ×(0, T)) only. In this case the classical Krushkov condition can make no sense because of unboundedness of u, if no growth condition on is assumed. This obstacle

is overcome by introducing the so-called renormalized entropy solution generalizing the classical one. Existence and uniqueness of such a solution is established.

Item Type: | Article |
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Uncontrolled Keywords: | Nonlinear semigroup theory; Cauchy problem; mild solutions; Renormalized ntropy sub- and super-solutions |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15861 |

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Deposited On: | 09 Jul 2012 09:43 |

Last Modified: | 06 Feb 2014 10:33 |

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