Equacions en derivades parcials i sistemes dinàmics.

The project belongs to the field of partial differential equations considered from the point of view of the dissipative dynamical systems. Many initial boundary value problems for partial differential equations have solutions that are susceptible of being considered as trajectories in function spaces. For these problems it is natural to try to extend the qualitative theory of ordinary differential equations (estability of equilibria, Lyapunov functions, existence of attracting invariant manifolds and of global attracting sets, structural stabillity, etc.) and the main difficulty arises from the infinite dimensionality of the states space. The project aims at contributing to the development of this approach through the study of some problems that have proved the interest of it. From one hand, the dynamics of parabolic equations, for which there a complete description in some cases, based