Well-posedness of a conservation law with non-local flux arising in traffic flow modeling. (English) Zbl 1336.65130
A well-posedness result of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling is proved. The obtained result provides accurate \(L^\infty\), BV and \(L^1\) estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 90B20 | Traffic problems in operations research |
| 35D30 | Weak solutions to PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
well-posedness; entropy weak solution; conservation law; non-local flux; Lax-Friedrichs scheme; traffic flow modelingReferences:
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