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Data assimilation for the time-dependent transport problem. (English) Zbl 0957.35021

Bojarski, Bogdan (ed.) et al., Evolution equations. Existence, regularity and singularities. Proceedings of the minisemester, Warsaw, Poland, September 21-October 2, 1998. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 52, 213-220 (2000).
The data assimilation problem for a time-dependent transport problem in a slab when the initial condition is not known is considered. The spaces of traces are introduced, the solvability of the original initial-boundary value transport problem is studied. The properties of the control operator are investigated and the solvability of the data assimilation problem is proved. The class of iterative methods for solving the problem is considered, and the convergence conditions are studied.
For the entire collection see [Zbl 0942.00027].

MSC:

35B37 PDE in connection with control problems (MSC2000)
65K10 Numerical optimization and variational techniques
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