# Data assimilation for the time-dependent transport problem

Banach Center Publications (2000)

- Volume: 52, Issue: 1, page 213-220
- ISSN: 0137-6934

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topShutyaev, Victor. "Data assimilation for the time-dependent transport problem." Banach Center Publications 52.1 (2000): 213-220. <http://eudml.org/doc/209059>.

@article{Shutyaev2000,

abstract = {In this paper we consider the data assimilation problem for a timedependent transport problem in a slab when the initial condition is not known. 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, 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. The results are closely connected with some issues raised in [4], [14], [15].},

author = {Shutyaev, Victor},

journal = {Banach Center Publications},

keywords = {initial-boundary value transport problem; slab; spaces of traces; control operator; iterative methods; convergence conditions},

language = {eng},

number = {1},

pages = {213-220},

title = {Data assimilation for the time-dependent transport problem},

url = {http://eudml.org/doc/209059},

volume = {52},

year = {2000},

}

TY - JOUR

AU - Shutyaev, Victor

TI - Data assimilation for the time-dependent transport problem

JO - Banach Center Publications

PY - 2000

VL - 52

IS - 1

SP - 213

EP - 220

AB - In this paper we consider the data assimilation problem for a timedependent transport problem in a slab when the initial condition is not known. 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, 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. The results are closely connected with some issues raised in [4], [14], [15].

LA - eng

KW - initial-boundary value transport problem; slab; spaces of traces; control operator; iterative methods; convergence conditions

UR - http://eudml.org/doc/209059

ER -

## References

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- [10] J. L. Lions, Sur le Contrôle Optimal de Systèmes Gouvernés par des Equations aux Dérivées Partielles, Dunod, Paris, 1968.
- [11] G. I. Marchuk and V.I. Lebedev, Numerical Methods in the Theory of Neutron Transport, Harwood Academic Publisher, New York, 1986. Zbl0234.65102
- [12] S. Mischler, Equation de Vlasov avec régularité Sobolev du champ: théorèmes de trace et applications, preprint No.13, Université de Versailles, 1997.
- [13] V. P. Shutyaev, Necessary and sufficient conditions of solvability of the initial-boundary value transport problem, in: Mathematical Models of Non-Linear Excitation, Transport, Dynamics, Control in Condensed Systems and other Media, Proc. of the Third International Conf. Tver 1998, V. Mironov (ed.), TGTU, Tver, 1998, 180.
- [14] V. P. Shutyaev, On a class of insensitive control problems, Control and Cybernetics 23 (1994), 257-266. Zbl0809.93022
- [15] V. P. Shutyaev, Some properties of the control operator in the problem of data assimilation and iterative algorithms, Russ. J. Numer. Anal. Math. Modelling 10 (1995), 357-371. Zbl0840.65040
- [16] V. P. Shutyaev, Some regularity properties of the solution of the time-dependent transport-problem in a slab, preprint No.81, Dept. Numer. Math., USSR Academy of Science, 1985 (in Russian).
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