Elliptic and parabolic partial differential equations on networks and applications

Master thesis written under the supervision of Olivier Ley and Francsico Silva. We study elliptic partial differential equations posed on networks. We prove that linear elliptic operators on networks are infinitesimal generators of strongly continuous semigroups. We then consider applications to parabolic PDEs and we also study the Feller property of the semigroup and study its associated stochastic process.