The delta standing wave solution for the linear scalar conservation law with discontinuous coefficients using a self-similar viscous regularization
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1945-1962
Published online November 30, 2015
Xiumei Li and Chun Shen
Ludong University, Ludong University
Abstract : 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 vanishing 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 solution 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.
Keywords : linear flux function, discontinuous coefficient, delta standing wave, viscosity vanishing method, Riemann problem, scalar conservation law
MSC numbers : 35L65, 35L67, 76N15
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