Thesis Summary:

In this work we study and analyze basic concepts of conservation laws, as well as review the basic theory of finite volume methods. Later we study conservation laws with a constant constraint [1] and with non-local constraint [2] from the analytical point of view and their numerical approximation using first and second order schemes. Applications such as vehicular flow dynamics due to control measures (trafic lights, speed reduction, among others) or pedestrian dynamics with constraint in the flow of output are studied for these models. Finally, we study the entropy solution of an EDO-EDP [13] coupling problem, with which the presence of a slow vehicle on the road is modeled, affecting fast vehicles.