Contractive relaxation systems and the scalar multidimensional conservation law

Katsoulakis, Markos A.; Tzavaras, Athanasios E.

doi:10.1080/03605309708821261

Cited by 84 publications

(74 citation statements)

References 14 publications

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“…Under the hypotheses (28), (29), the entropy solution can be expressed by means of generalized characteristics, cf [11] and also [35].…”

Section: Some Results About Initial-boundary-value Problemsmentioning

confidence: 99%

“…[t, t + ]) for some > 0. It can be proved that for a given entropy solution of (27), (28), (29), there exists at least one forward and backward characteristic at each point x, t.…”

Section: Definition 1 a Generalized Characteristic Associated To Thementioning

confidence: 99%

“…For simplicity only, we suppose from now on that B ≡ 1 in order to be able to use the explicit formulas (17). The next step is to study the properties of a relaxing scheme in the sense of [28,29] based on local Riemann problems of the type (12), (15), (18). More precisely, given any initial data (w 0 , z 0 ) in L 1 ∩ BV (R) and a space-step h > 0, we define the following sequences for j ∈ Z:…”

Section: Lemmamentioning

confidence: 99%

“…We will focus on two significant examples. The first one is the special case of relaxation approximation to the scalar conservation law (1)- (2), [28,29]. The second one corresponds to the general case of a scalar balance law (26).…”

Section: Introductionmentioning

confidence: 99%

“…Motivation. We are interested in studying relaxation approximations in the sense of [28,29] to the entropy solution of the scalar conservation law:…”

Section: Introductionmentioning

confidence: 99%

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Localization effects and measure source terms in numerical schemes for balance laws

Gosse

2001

Math. Comp.

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Abstract. This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

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“…Under the hypotheses (28), (29), the entropy solution can be expressed by means of generalized characteristics, cf [11] and also [35].…”

Section: Some Results About Initial-boundary-value Problemsmentioning

confidence: 99%

“…[t, t + ]) for some > 0. It can be proved that for a given entropy solution of (27), (28), (29), there exists at least one forward and backward characteristic at each point x, t.…”

Section: Definition 1 a Generalized Characteristic Associated To Thementioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Motivation. We are interested in studying relaxation approximations in the sense of [28,29] to the entropy solution of the scalar conservation law:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations