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Optimization of hyperbolic systems under nonlocal boundary conditions of Bitsadze-Samarskiĭ type. (English. Russian original) Zbl 0615.35005

Sov. Math., Dokl. 32, 183-187 (1985); translation from Dokl. Akad. Nauk SSSR 283, 787-791 (1985).
Interest in local and nonlocal boundary value problems for loaded integrodifferential equations has increased substantially in recent years in connection with investigations of problems involving optimal control of agro-ecological systems. In this context we shall consider some classes of local and nonlocal optimization problems for loaded hyperbolic equations with deviating argument. It is shown that such problems can be investigated with the help of variational derivatives of a special kind whose use is connected with the introduction of supplementary Lagrange multipliers which take into account the nonlocal property of the original problem.

MSC:

35B37 PDE in connection with control problems (MSC2000)
35R10 Partial functional-differential equations
35L70 Second-order nonlinear hyperbolic equations
49K20 Optimality conditions for problems involving partial differential equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems