Answers are grounded in this paper and cite their sources.
We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal locations. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L¹, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken from [K. H. Karlsen, N. H. Risebro, and J. D. Towers, Skr. K. Nor. Vidensk. Selsk., 3 (2003), pp. 1--49], we show that the solution operator is L 1 contractive. These results generalize the corresponding results from [S. N. Kruzkov, Math. USSR-Sb., 10 (1970), pp. 217--243] and also partially those from Karlsen, Risebro, and Towers.
No takes yet. Share an insight, caveat, or question.
Coclite et al. (2005) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: