Keyword: 1991 MR Subject Classification 35A35 : Search

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Keyword: 1991 MR Subject Classification 35L65 (3)	26 Mar 2025	Run
Keyword: 1991 MR Subject Classification 35A35 (2)	26 Mar 2025	Run
Keyword: 1991 MR Subject Classification 35L45 (2)	26 Mar 2025	Run
Keyword: Probability Density Evolution Method (9)	26 Mar 2025	Run
Keyword: Breeden-litzenberger Theorem (1)	26 Mar 2025	Run

articleNo Access
ON THE CONVERGENCE OF GODUNOV SCHEME FOR NONLINEAR HYPERBOLIC SYSTEMS
- A. BRESSAN and
- H. K. JENSSEN
Chinese Annals of Mathematics01 Jul 2000
Preview Abstract
The authors consider systems of the form
where the matrix A(u) is assumed to be strictly hyperbolic and with the property that the integral curves of the eigenvector fields are straight lines. For this class of systems one can define a natural Riemann solver, and hence a Godunov scheme, which generalize the standard Riemann solver and Godunov scheme for conservative systems. This paper shows convergence and L¹ stability for this scheme when applied to data with small total variation. The main step in the proof is to estimate the increase in the total variation produced by the scheme due to quadratic coupling terms. Using Duhamel's principle, the problem is reduced to the estimate of the product of two Green kernels, representing probability densities of discrete random walks. The total amount of coupling is then determined by the expected number of crossings between two random walks with strictly different average speeds. This provides a discrete analogue of the arguments developed in [3,9] in connection with continuous random processes.
articleNo Access
ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS
- T. GALLOUËT and
- F. HUBERT
Chinese Annals of Mathematics01 Jan 1999
Preview Abstract
The authors give a proof of the convergence of the solution of the parabolic approximation towards the entropic solution of the scalar conservation law u_t + div f(x, t, u)=0 in several space dimensions. For any initial condition u₀ ∈ L^∞(ℛ^N) and for a large class of flux f, they also prove the strong converge in any space, using the notion of entropy process solution, which is a generalization of the measure-valued solutions of DiPerna.