We consider a problem of optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and semidefinite quality criterion. The optimality conditions are constructed by reducing the problem to a sequence of one-dimensional problems, the optimal control is obtained in a closed form, and its convergence is proved. The form of the quality criterion is substantiated.
The article applies a unified approach to examine two types of problems: dynamic inverse problem and robust control problem. Two types of models are considered: a dynamical model linking the main economic and climatic variables and a model describing the interaction of climate with the biosphere. The study is relevant also for other classes of models: the phase field equation, a fed bioreactor, and...
Origin of asymptotics of different orders and an algorithm for choosing the best asymptotics are shown by examples, which allow us to obtain a priori estimates of solutions to control boundary-value problems, exact in the order of a small parameter.
Formal algorithms for complete asymptotic decompositions of solutions to optimal globally bounded control problems for elliptic equations with fast oscillating coefficients are constructed. If the kernel of a differential operator of the initial problem is nonzero, asymptotics of different orders may exist in the control system.
We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.
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