Renormalized entropy solutions of scalar conservation laws
Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Lucio Boccardo, Thierry Gallouët, Luigi Orsina (1996)
Annales de l'I.H.P. Analyse non linéaire
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Fuensanta Andreu, Vicent Caselles, José Mazón (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions...
Sergio Segura de León, José Toledo (1999)
Publicacions Matemàtiques
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In this note we give some summability results for entropy solutions of the nonlinear parabolic equation u - div a (x, ∇u) = f in ] 0,T [xΩ with initial datum in L(Ω) and assuming Dirichlet's boundary condition, where a(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L (]0,T[xΩ) and Ω is a domain in R. We find spaces of type L(0,T;M(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...
Tero Kilpeläinen, Xiangsheng Xu (1996)
Revista Matemática Iberoamericana
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We discuss the uniqueness of solutions to problems like ⎧ λ |u|s-1u - div (|∇u|p-2∇u) = μ on Ω, ⎨ ⎩ u = 0 in ∂Ω, where λ ≥ 0 and μ is a signed Radon measure.
Laurent Levi (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in . Lastly, we study the behaviour of this solution and its stability properties...