Delta‐shock for a class of systems of conservation laws of the Keyfitz–Kranzer type

Abstract

AbstractRiemann problem for a class of systems of conservation laws of Keyfitz–Kranzer type is solved. The Riemann solutions contain three kinds of interesting structures, two of which contain vacuum and the other includes delta‐shock. The generalized Rankine–Hugoniot relation and improved entropy condition are proposed to solve the delta‐shock. Besides, with the use of the vanishing viscosity method, all of the existence, uniqueness, and stability of the solutions involving the delta‐shock are proved.