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Numerical optimization of solutions to Burgers problem by means of boundary conditions. (English. Russian original) Zbl 0947.90123
Comput. Math. Math. Phys. 37, No. 12, 1406-1414 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 12, 1449-1458 (1997).
The authors propose a method for solving an optimal control problem for Burger’s equation. The boundary conditions of the problem are used as a control, and the functional is given by the integral norm of the deviation of the solution to Burger’s equation from a certain experimental function. In the continuous case, the gradient of the functional is obtained in terms of the solution to the conjugate problem. The gradient of the functional of the discretized problem is calculated exactly, and the approximation scheme for the conjugate problem is determined automatically.

90C52 Methods of reduced gradient type
65K05 Numerical mathematical programming methods
76M30 Variational methods applied to problems in fluid mechanics