ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65 Palencia, C., and J. M. Marbán, Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Spain A numerical method for the integration of backward parabolic problems Let A : D(A) ⊂ X → X be the infinitesimal generator of an analytic semigroup in a Banach space. Given T > 0 and u_{T} ∈ X the backward Cauchy problem

u′(t) = Au(t), 0 ≤ t ≤ T; u(T) = u_{T}

is considered. This problem is severely ill posed: the solution, assuming that it exists, does not depend continuously on u_{T}. The problem is regularized by means of an a priori estimate of the form ∥u(t)∥ ≤ M, for 0 ≤ t ≤ T. A new method for the discretization of such problem is proposed. The method is based on a new algorithm for recovering an analytic mapping from a discrete set of corrupted samplig values.