Resumen de Cauchy problems with periodic controls
István Gyöngyi, Nicolai Krylov
For each 2 (0, 1] the Cauchy problem dw(t) = m Xk=1 (Lkw(t) + fk)dHk(t/ ), t 0, w(0) = w0 in a Banach space V is considered, where L1, ...,Lm are linear unbounded operators on V , w0, f1, ..., fk 2 V , and H1, ...,Hm are rightcontinuous functions on R having finite variation on each finite interval, such that dHk are invariant with respect to some fixed shift. For the solution an expansion in powers of is obtained. Applications to numerical solutions of PDEs are presented. In particular, it is shown that the order of accuracy of finite di erence and splitting-up approximations can be made as high as wanted by an implementation of Richardson¿s idea.
