ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS

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CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX (2004, result): “1) when k = k(x) is allowed to be discontinuous, some other results can be found in [18, 16, 33, 28].”
A Hamilton-Jacobi approach to junction problems and application to traffic flows (2011, unknown): “On the other hand, the analysis of scalar conservation laws with discontinuous ﬂux functions has been extensively studied, we refer to [32, 3, 10] and references therein.”
Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients (2006, background): “It has been proven in different works (Bachmann, 2004; Karlsen and Risebro, 2001; Karlsen et al., 2002b; Seguin and Vovelle, 2003; Towers, 2000) that this notion of entropy solution allows to show that existence, uniqueness, consistence with approximations holds.”
Some approximate Godunov schemes to compute shallow-water equations with topography (2003, methodology): “In a conservative framework, the second-order scheme with the classical reconstruction converges but the speed of convergence slows down compared with both other schemes (see [26]).”