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## Banach Center Publications

2000 | 52 | 1 | 213-220
Tytuł artykułu

### Data assimilation for the time-dependent transport problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
213-220
Opis fizyczny
Daty
wydano
2000
Twórcy
autor
• Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkin St. 8, 117951, Moscow, Russia
Bibliografia
• [1] V. I. Agoshkov, Boundary Value Problems for Transport Equations, Birkhäuser, Boston, 1998.
• [2] V. I. Agoshkov, Necessary and sufficient conditions for solvability of some first-order hyperbolic problems, preprint No.248, Dept. Numer. Math., USSR Academy of Science, 1990 (in Russian).
• [3] V. I. Agoshkov, On existence of traces of functions in spaces used in transport theory, Soviet Doklady 288 (1986), 265-269.
• [4] V. I. Agoshkov and G. I. Marchuk, On the solvability and numerical solution of data assimilation problems, Russ. J. Numer. Anal. Math. Modelling 8 (1993), 1-16.
• [5] C. Bardos, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport, Ann. Scient. Ec. Norm. Sup. 4 (1970), 185-233.
• [6] M. Cessenat, Théorèmes de trace $L^p$ pour les espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris 299 (1984), 831-834.
• [7] T. A. Germogenova, Local properties of solutions of the transport equation, Sov. Doklady 187 (1969), 18-21.
• [8] T. A. Germogenova, Local Properties of Solutions of Transport Equations, Nauka, Moscow, 1986.
• [9] W. Greenberg, C. Van der Mee, and V. Protopopescu, Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser, Basel, 1987.
• [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.
• [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.
• [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.
• [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).
• [17] S. Ukai, Solutions of the Boltzmann equations, in: Patterns and Waves-Qualitative Analysis of Nonlinear Differential Equations, Stud. Math. Appl. 18, North-Holland, Amsterdam (1986), 37-96.
• [18] V. S. Vladimirov, Mathematical problems of one-velocity transport theory, Proc. of the Steklov Inst. Math. 61, 1961.
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Bibliografia
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