Concept of Delta-shock Type Solutions to Systems of Conservation Laws and the Rankine–Hugoniot Conditions

DOI10.1007/978-3-0348-0585-8_16zbMath1263.35163OpenAlexW123915855MaRDI QIDQ4914479

Vladimir Shelkovich

Publication date: 12 April 2013

Published in: Pseudo-Differential Operators, Generalized Functions and Asymptotics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0585-8_16

zbMATH Keywords

Rankine-Hugoniot conditionsintegral identities\(\delta\)-shocks

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Hyperbolic conservation laws (35L65)

Related Items

The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach) ⋮ Classical solutions to the relativistic Euler equations for a linearly degenerate equation of state ⋮ A numerical scheme for singular shock solutions and a study of its consistence in the sense of distributions ⋮ Formation and propagation of singularities in one-dimensional Chaplygin gas

Cites Work

• Study of the system of quasilinear equations for isotachophoresis
• Interactions of delta shock waves in a strictly hyperbolic system of conservation laws
• Mass, momentum and energy conservation laws in zero-pressure gas dynamics and δ-shocks: II
• Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks
• Non-classical shallow water flows
• $ \delta$- and $ \delta'$-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes
• Formation of density singularities in ideal hydrodynamics of freely cooling inelastic gases: A family of exact solutions
• Unnamed Item
• Unnamed Item
• Unnamed Item