This dissertation presents a synthesis of research articles devoted to the analysis of mathematical problems arising from fluid mechanics. In particular, with an approach including mathematical modelling, theoretical and numerical analysis of partial differential equations and scientific computing, the application fields of these studies have focused on two major subjects: thin film mechanics and life sciences. The dissertation contains three chapters which focus on 1) hydrodynamic lubrication, 2) scalar conservation laws on a bounded domain and 3) mathematical modelling applied to life sciences including two different topics: the modelling of the respiratory system (in particular gas exchange in the bronchial tree) and simulation of active or passive biomimetic suspensions in a viscous fluid.
