Optimal control of processes described by equations of hyperbolic type. (English. Russian original) Zbl 0438.49008
J. Appl. Math. Mech. 41(1977), 385-397 (1978); translation from Prikl. Mat. Mekh. 41, 387-398 (1977).
MSC:
49J20 | Existence theories for optimal control problems involving partial differential equations |
49M29 | Numerical methods involving duality |
35L20 | Initial-boundary value problems for second-order hyperbolic equations |
Keywords:
Bolza problemReferences:
[1] | Egorov, A. I., On the optimal control of processes in distributed plants, PMM, Vol. 28, N≗ 4 (1964) · Zbl 0135.33102 |
[2] | Petukhov, L. V.; Troitskii, V. A., Variational optimization problems for equations of hyperbolic type, PMM, Vol.36, N≗ 4 (1972) · Zbl 0261.49005 |
[3] | Petukhov, L. V.; Troitskii, V. A., Some optimal problems of the theory of longitudinal vibrations of rods, PMM, Vol.36, N≗ 5 (1972) · Zbl 0274.73032 |
[4] | Petukhov, L. V.; Troitskii, V. A., Variational problems of optimization for equations of the hyperbolic type in the presence of boundary controls, PMM, Vol. 39, N≗ 2 (1975) |
[5] | Kraiko, A. N., Variational problems of gas dynamics of nonequilibrium and equi- librium flows, PMM, Vol. 28, N≗ 2 (1964) · Zbl 0136.45702 |
[6] | Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics (1963), American Mathematical Society: American Mathematical Society Providence, (English translation) · Zbl 0123.09003 |
[7] | Ladyzhenskaia, O. A., Mixed Boundary-Value Problem for a Hyperbolic Equation (1953), Gostekhizdat: Gostekhizdat Moscow |
[8] | Rashevskii, P. K., Riemann Geometry and Tensor Analysis (1967), Nauka: Nauka Moscow · Zbl 0186.06502 |
[9] | Smirnov, V. I., Course of Higher Mathematics, (Book N≗ 10207, Vol. 2 (1964), Pergamon Press), (English Translation) · Zbl 0122.29703 |
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