RESUMEN

The evolution of a physical system in time is generally described by an initial value problem for an (abstract) differential equation of the form

du (t) / dt = Au (t) (t >= 0),    u (0) = f.    (*)

Here the function u takes values in a space * , f ε * , and A is an operator with domain and range in * ; we shall only deal with the (special) case that * is a Banach space and A is a (typically unbounded) linear operator on *. In the applications A is a partial variables x₁ , … , x_{n ;} there are also boundary conditions which are taken into account when specifying the domain of A.