Delta shock wave as limits of vanishing viscosity for zero‐pressure gas dynamics with energy conservation law

Li, Shiwei

doi:10.1002/zamm.202100377

Z Angew Math Mech

2022

DOI: 10.1002/zamm.202100377

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Delta shock wave as limits of vanishing viscosity for zero‐pressure gas dynamics with energy conservation law

Shiwei Li

Abstract: This paper studies the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. By the vanishing viscosity method, the stability of the solutions involving delta shock wave with Dirac delta functions developing in both state variables is established.

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2023

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References 31 publications

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Riemann problem for a $2\times 2$ hyperbolic system with time-gradually-degenerate damping

2023

Bound Value Probl

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This paper is focused on the Riemann problem for a $2\times 2$ 2 × 2 hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.

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Riemann problem for a $2\times 2$ hyperbolic system with time-gradually-degenerate damping

2023

Bound Value Probl

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Delta shock wave as limits of vanishing viscosity for zero‐pressure gas dynamics with energy conservation law

Abstract: This paper studies the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. By the vanishing viscosity method, the stability of the solutions involving delta shock wave with Dirac delta functions developing in both state variables is established.

Cited by 1 publication

References 31 publications

Riemann problem for a $2\times 2$ hyperbolic system with time-gradually-degenerate damping

Riemann problem for a $2\times 2$ hyperbolic system with time-gradually-degenerate damping

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