A notion of renormahzed solution of the study of a general conservation law.
PATRICK URRUTY (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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PATRICK URRUTY (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Guy Vallet (2000)
Revista Matemática Complutense
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In this paper we propose the study of a first-order non-linear hyperbolic equation in a bounded domain. We give a result of existence and uniqueness of the entropic measure-valued solution and of the entropic weak solution; for some general assumptions on the data.
M. Bouchekif (1994)
Publicacions Matemàtiques
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In this paper, we obtain some existence theorems of nonnegative solutions with compact support for homogeneous Dirichlet elliptic problems; we also extend these results to parabolis systems. Supersolution and comparison principles are our main ingredients.
P. L. Lions, B. Perthame (1989)
Annales de l'I.H.P. Analyse non linéaire
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Michael Hinze, Ulrich Matthes (2009)
Control and Cybernetics
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Ugo Gianazza, Giuseppe Savaré (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls....