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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 $(\rho,w)\in {\Bbb R}\times {\Bbb R}^n$ 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.

35L65Conservation laws
35B45A priori estimates for solutions of PDE
35D30Weak solutions of PDE
35A01Existence problems for PDE: global existence, local existence, non-existence
90B20Traffic problems
Full Text: DOI
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