Mathematical modelling of mechanics problems
Amosovа E.
The optimal control problem for the evolutionary Burgers equation
Abstract: The article deals with the extreme problem for the model equation of the motion of a viscous gas. The problem was formulated as an optimal control problem with non-local distributed control depending on time only. The existence of the solution was established and the necessary optimality conditions for the problem were obtained. The optimality system was built and substantiated and it made it possible to study the conditions of the finite aggregate of the solutions to the extreme problem as well as the conditions providing the uniqueness of the solution to the problem to be attacked.
Key words: optimum control, Byurgers's equation, optimality system, non-local control.
REFERENCES
- Belov S.Ja. Problems of optimum control of currents of viscous gas. Dynamics of continuous environment. Novosibirsk, 1983(60):34-50. (in Russ). [Belov S.Ja. Zadachi optimal'nogo upravlenija techenijami vjazkogo gaza // Dinamika sploshnoj sredy. 1983. Vyp. 60. S. 34-50].
- Fursikov A.V. Properties of solutions of some extreme tasks connected with Navier–Stokes's system. Mathematical proc. 1982(118);3:323-349. (in Russ). [Fursikov A.V. Svojstva reshenij nekotoryh jekstremal'nyh zadach, svjazannyh s sistemoj Nav'e-Stoksa // Mat. sb. 1982. T. 118, N 3. S. 323-349].
- Chebotarjov A.Ju. The principle of a maximum in a task of boundary management of a current of viscous liquid. Siberian mathematical j. 1993(34);6:202-213. (in Russ). [Chebotarjov A.Ju. Princip maksimuma v zadache granichnogo upravlenija techeniem vjazkoj zhidkosti // Sib. mat. zhurn. 1993. T. 34, N 6. S. 202-213].
- Fursikov А.V. On approximate controllability of the Stokes system. Ann. Fac. Sci. Toulouse Math. 1993(11);2:205-232.
- Lions J.L. Control of systems governed by partial differential equations. New York, Springer-Verlag, 1972.
- Stritharan S.S. Dynamic programming of the Navier–Stokes equations. Systems Control Lett. 1991(6):299-307.
- White L.W. Study of uniqueness for the initialization problem for Burger's equation. J. Math. Anal, and Appl. 1993(172):412-431.