Abstract
This paper is devoted to a scalar conservation law with a linear flux function involving discontinuous coefficients. It is clear that the delta standing wave should be introduced into the Riemann solution in some nonclassical situation. In order to study the formation of delta standing wave, we consider a regularization of the discontinuous coefficient with the Helmholtz mollifier and then obtain a regularized system which depends on a regularization parameter ɛ > 0. The regularization mechanism is a nonlinear bending of characteristic curves that prevents their finite-time intersection. It is proved rigorously that the solutions of regularized system converge to the delta standing wave solution in the ɛ → 0 limit. Compared with the classical method of vanishing viscosity, here it is clear to see how the delta standing wave forms naturally along the characteristics.
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