Connecting orbits in Hilbert spaces and applications to P.D.E.

Abstract: Functional Analysis methods are often useful to solve efficiently P.D.E. problems. The idea is to view a solution of a P.D.E. as a map with values in a space of functions, and reduce the initial P.D.E. to an O.D.E. problem. I will establish a general theorem on the existence of heteroclinic orbits in Hilbert spaces. As a first application, I will present a new construction, in a more general setting, of the heteroclinic double layers  (initially constructed by Schatzman). As a second application, I will show the existence of the heteroclinic double layers for a fourth order P.D.E.