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 |