Symmetries of systems with spatially bounded domains

This paper deals with the investigation of the dynamics occurring in a 1-dimensional linear second-order partial differential equation. Our main focus is the investigation of the effects produced on these dynamics by both reflection and translation symmetry-breakings in bounded domains. This is performed by considering two different sets of boundary conditions, first Robin, and then periodic, along with the presence of an advection term. Dynamical systems like this are widely encountered in several fields of applied science. In particular, in Theoretical Physics, they describe a diffusive problem in the presence of throughflow, driven by a forcing. Often this kind of system constitutes the grounds for nonlinear problems where persistent travelling waves are observed. In the present work major focus is given to the investigation of the eventual occurrence of time-dependent solutions via Hopf bifurcation.