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Renormalized entropy solutions of scalar conservation laws.

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
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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