Dynamics of Delta Shock Waves Originating From a Three‐Piece Riemann Problem for Traffic Flow Model

ABSTRACT This article addresses the interactions of delta shock waves with elementary waves in a strictly hyperbolic system of conservation laws derived from a traffic flow model. On utilizing the technique of splitting delta function, the global structures of solutions are constructed and analyzed one by one. Moreover, we prove that the solutions of the Riemann problems are stable under the small perturbations of the Riemann data.