Delta-shock waves as self-similar viscosity limits

Ercole, Grey

doi:10.1090/qam/1739044

Cited by 41 publications

(47 citation statements)

References 15 publications

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“…More precisely, we will prove that (v ε ) ε converges to a distribution containing δ distribution. This is in accordance with the previous result on this subject (see [10,14,16,17,31] and many others).…”

Section: Introductionsupporting

confidence: 94%

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Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Mitrović

Bojković

Данилов

2010

Math Methods in App Sciences

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Abstract. We generalize procedure from [28] on the case of more general triangular system of conservation laws arising from so called generalized pressureless gas dynamics. Using the weak asymptotic method [10,12], more precisely nonlinear superposition law [8], we approximate the nonlinear system by a linear one. Then, we can use usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how delta shock wave naturally arises along the characteristics.

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Section: Introductionsupporting

confidence: 94%

“…This Riemann problem is intensively investigated in recent years [7,10,11,13,14,16,17,18,19,21,24,28,30,31,32,36,37,39] (the list is far from being complete). The reason for this lies in applicability of the system -it arises from (generalized) pressureless gas dynamics [3,27].…”

Section: Introductionmentioning

confidence: 99%

Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Mitrović

Bojković

Данилов

2010

Math Methods in App Sciences

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“…As in [10], [14], [26], to solve the Cauchy problems (1.1), (1.13) or (1.9), (1.14), we shall use the "overcompression" condition (for details, see [17]):…”

Section: Delta-shock Wave Type Solution 407mentioning

confidence: 99%

Untitled

2005

Quart. Appl. Math.

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Abstract. For two classes of hyperbolic systems of conservation laws new definitions of a δ-shock wave type solution are introduced. These two definitions give natural generalizations of the classical definition of the weak solutions. It is relevant to the notion of δ-shocks. The weak asymptotics method developed by the authors is used to describe the propagation of δ-shock waves to the three types of systems of conservation laws and derive the corresponding Rankine-Hugoniot conditions for δ-shocks.

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“…All of the existence, uniqueness, and stability of solutions were investigated to viscous perturbations. See also Yang [12] for the generalized zeropressure system and [13][14][15][16][17][18][19][20][21][22][23] for the viscosity vanishing approach on various systems of conservation laws.…”

Section: Introductionmentioning

confidence: 99%

Vanishing viscosity limit for Riemann solutions to zero-pressure gas dynamics with flux perturbation

Zhang

Junchao

2018

Bound Value Probl

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In this paper, by the viscosity vanishing approach, we consider the Riemann problem for zero-pressure gas dynamics with flux perturbation. The Riemann solutions involve parameterized delta shock wave and constant density state. For the parameterized delta-shock solution, its generalized Rankine-Hugoniot and entropy condition are clarified. While for the constant density solution, the formation of it is rigorously analyzed. Moreover, all of their existence, uniqueness, and stability to reasonable viscous perturbations are shown.

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Delta-shock waves as self-similar viscosity limits

Cited by 41 publications

References 15 publications

Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Untitled

Vanishing viscosity limit for Riemann solutions to zero-pressure gas dynamics with flux perturbation

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