Résumé
A mathematical analysis, based on the theory of semi-groups of operators on Hilbert space, of linearized problems involving Saint-Venant equations governing shallow water flows is carried out. The first problem concerns the classical linearized Saint-Venant problem, while the second deals with a water quality problem: the evolution of a concentration of products in a flow solution of the first problem. The method seems capable to take into account thermal and multi-phase effects.