Melnik, (R.)V.N.
In this paper we treat mathematical and computational models of thermodynamical systems in complex media as optimal information control problems. Under assumptions of sufficient smoothness on the perturbed Hamiltonian of the system, we propose reformulations of the classical problems using the concept of informational limit. In the general situation, we use Steklov's operator technique to derive generalizations of classical Hamilton-Jacobi-Bellman (HJB) equations in stochastic, non-smooth, and deterministic cases. We show that a non-conservation law equation appears naturally from such a consideration. For its approximation we use an evolution-associated Markov chain which permits us to derive stability conditions for our computational models. The computational models of this type give a description of generalized dynamical systems (GDS) which include the modeler (decision maker, DM) as an intrinsic part. Several application examples are discussed in the context of multilayered structures such as superlattices where we have to deal with mathematical models with discontinuous characteristics.
Key words: non-conservation law models; generalized dynamical systems; Steklov's operators; evolution-associated Markov chains; Hamilton-Jacobi-Bellman equations; thermodynamical systems; optimal control; stochastic, non-smooth, and determinsitic mathematical models; informational limit; perturbed Hamiltonian; Feer's sums; L1 norms.
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