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This paper analyzes a two-by-two Temple-type system of conservation laws with discontinuous flux, focusing on applications in traffic modeling. We prove the existence of entropy solutions for initial data with sufficiently small total variation. Additionally, we explicitly construct the corresponding Riemann solver and examine its key properties. To illustrate the impact of the discontinuous flux on the solution, we also present numerical simulations.

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for periodic initial data having finite total variation and initial density bounded away from zero.

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in [2] to the Cauchy problem for any $BV$ initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast., Comment: 31 pages, 2 figures