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Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type. (English) Zbl 1235.35194

The author studies the Cauchy problem for nonsymmetric systems of Keyfitz-Kranzer type \[ \rho_t+(\rho\phi(\rho,w))_x=0, \quad (\rho w)_t+(\rho w\phi(\rho,w))_x=0, \] where the unknown vectors \((\rho,w)\in {\mathbb R}\times {\mathbb R}^n\) and \(\phi(\rho,w)=\Phi(w)-P(\rho)\). In the case \(n=1\), \(\Phi(w)=w\), this system coincides with the known Aw-Rascle traffic flow model. Using BV estimates on the Riemann invariants and the compensated compactness method applied to special approximate sequences, the author establishes the global existence of bounded entropy weak solutions.

MSC:

35L65 Hyperbolic conservation laws
35B45 A priori estimates in context of PDEs
35D30 Weak solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
90B20 Traffic problems in operations research
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