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This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity van- ishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave so- lution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.

THE DELTA STANDING WAVE SOLUTION FOR THE LINEAR SCALAR CONSERVATION LAW WITH DISCONTINUOUS COEFFICIENTS USING A SELF-SIMILAR VISCOUS REGULARIZATION