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Dafermos, C.M. (1972) Polygonal Approximations of the Initial Value Problem for a Conservation Law. Journal of Differential Equations, 38, 33-41.
https://doi.org/10.1016/0022-247X(72)90114-X

has been cited by the following article:

• TITLE: Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

  AUTHORS: Yihong Dai, Jing Zhang

  KEYWORDS: Scalar Conservation Laws with Weak Discontinuous Flux, Initial-Boundary Value Problem, Elementary Wave, Interaction, Structure of Global Weak Entropy Solution

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.7 No.4, December 14, 2017

  ABSTRACT: This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.