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 , … , xn ; there
are also boundary conditions which are taken into account when specifying the
domain of A.