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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Displaying similar documents to “An -theory of existence and uniqueness of solutions of nonlinear elliptic equations”
Renormalized entropy solutions of scalar conservation laws
Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
Lucio Boccardo, Thierry Gallouët, Luigi Orsina (1996)
Annales de l'I.H.P. Analyse non linéaire
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A strongly degenerate quasilinear equation : the elliptic case
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...
Regularity for entropy solutions of parabolic p-Laplacian type equations.
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...
On the uniqueness problem for quasilinear elliptic equations involving measures.
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.
Obstacle problems for scalar conservation laws
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...