Embedded delta shocks. Issue 6 (June 2020)

• Record Type: Journal Article
• Authors: Castañeda, Pablo
• Is Part Of: Heliyon. Volume 6:Issue 6(2020)
• Publication Date: 2020-06
• Subjects: Applied mathematics -- Theoretical fluid dynamics -- Mathematical analysis -- Magnetohydrodynamics -- Chromatography -- Conservation laws -- Riemann problem -- Delta shock -- Singular solutions -- Rankine-Hugoniot -- Two-phase flow; Research -- Periodicals; Medical sciences -- Periodicals; Natural history -- Periodicals; Social sciences -- Periodicals; Earth sciences -- Periodicals; Physical sciences -- Periodicals; 507.2
• DOI: 10.1016/j.heliyon.2020.e04152
• Languages: English
• ISSNs: 2405-8440

Abstract

Abstract: In 1977 Korchinski presented a new type of shock discontinuity in conservation laws. These singular solutions were coined δ -shocks since there is a time dependent Dirac delta involved. A naive description is that such δ -shock is of the overcompressive type: a single shock wave belonging to both families, the four characteristic lines of which impinge into the shock itself. In this work, we open the fan of solutions by studying two-family waves without intermediate constant states but possessing central rarefactions or comprising δ -shocks. Abstract : Applied mathematics; Theoretical fluid dynamics; Mathematical analysis; Magnetohydrodynamics; Chromatography; Conservation laws; Riemann problem; Delta shock; Singular solutions; Rankine-Hugoniot; Two-phase flow