Keyword: 1991 MR Subject Classification 35L65 : 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
ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN
- L. LÉVI and
- G. VALLET
Chinese Annals of Mathematics01 Jan 2001
Preview Abstract
This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of ℝ^p, p≥1.
The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L^∞-estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L^∞. The uniquess of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in L^q of approximate solutions of U.
articleNo Access
NONLINEAR STABILITY OF TWO-MODE SHOCK PROFILES FOR A RATE-TYPE VISCOELASTIC SYSTEM WITH RELAXATION
- LING HSIAO and
- RONGHUA PAN
Chinese Annals of Mathematics01 Oct 1999
Preview Abstract
The authors study a 3 × 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 × 2 quasi-linear hyperbolic system, including the well-known p-system. The nonlinear stability of two-mode shock waves in this relaxation approximation is proved.