Delta-shock wave type solution of hyperbolic systems of conservation laws

Abstract

For two classes of hyperbolic systems of conservation laws new definitions of a δ \delta -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 \delta -shocks. The weak asymptotics method developed by the authors is used to describe the propagation of δ \delta -shock waves to the three types of systems of conservation laws and derive the corresponding Rankine–Hugoniot conditions for δ \delta -shocks.