Cauchy problems with periodic controls

• Autores: István Gyöngyi, Nicolai Krylov
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 57, Fasc. Extra 1, 2006 (Ejemplar dedicado a: Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations), págs. 255-273
• Idioma: español
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• Resumen

  • 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.

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