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On the existence and compactness of a two-dimensional resonant system of conservation laws. (English) Zbl 1165.35412

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.

MSC:

35L65 Hyperbolic conservation laws
35L80 Degenerate hyperbolic equations

Citations:

Zbl 1084.35045
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