Karlsen, Kenneth H.; Rascle, Michel; Tadmor, Eitan On the existence and compactness of a two-dimensional resonant system of conservation laws. (English) Zbl 1165.35412 Commun. Math. Sci. 5, No. 2, 253-265 (2007). Summary: We prove the existence of a weak solution to a two-dimensional resonant \(3\times 3\) system of conservation laws with BV initial data. Due to possible resonance (coinciding eigenvalues), spatial BV estimates are in general not available. Instead, we use an entropy dissipation bound combined with the time translation invariance property of the system to prove existence based on a two-dimensional compensated compactness argument adapted from [E. Tadmor, M. Rascle and P. Bagnerini, J. Hyperbolic Differ. Equ. 2, No. 3, 697–712 (2005; Zbl 1084.35045)]. Existence is proved under the assumption that the flux functions in the two directions are linearly independent. Cited in 15 Documents MSC: 35L65 Hyperbolic conservation laws 35L80 Degenerate hyperbolic equations Keywords:discontinuous fluxes; entropy bounds; BV initial data; translation invariance property; compensated compactness argument Citations:Zbl 1084.35045 PDFBibTeX XMLCite \textit{K. H. Karlsen} et al., Commun. Math. Sci. 5, No. 2, 253--265 (2007; Zbl 1165.35412) Full Text: DOI arXiv Euclid