Abstract:
A feature of the general Lagrange multiplier method as applied to variational problems is studied in the case when a part of the boundary of the domain of the state variables and control functions is a characteristic of the system of governing partial differential equations. It is shown that, if the state variables and the control functions are not related on this boundary part and do not influence the objective functional value, then the compatibility conditions for the system of governing equations do not need to be taken into account in varying the functional. Otherwise, the compatibility conditions along the characteristic have to be included in the generalized Lagrange functional with their own multipliers.
Key words:variational problem, first variation of functional, gradient, the adjoint equations, characteristics.
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