Computer modelling of physical processes described by parabolic type equations

On Solvability of the Nonlinear Optimal Control Problem for Processes Described by the Semi-linear Parabolic Equations

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

Evolution Equations of Parabolic Type

be linear and quasilinear evolution equations of parabolic type in a Banach space X respectively. By "parabolic type" we mean that A(t) and A(t,u) are all the infinitesimal generators of analytic linear semigroups on X we do not necessarily assume that the domains of the operators A(t) and A("t,u) are dense subspaces of X, so the semigroups generated by them may not be of class c0 J. The domain...

Stochastic Processes and Perturbationproblems Defined by Parabolic Equations Witha Small

Markov processes and parabolic partial differential equations

In the first part of this article, we present the main tools and definitions of Markov processes’ theory: transition semigroups, Feller processes, infinitesimal generator, Kolmogorov’s backward and forward equations and Feller diffusion. We also give several classical examples including stochastic differential equations (SDEs) and backward SDEs (BSDEs). The second part of this article is devote...

Computer Modelling of Cognitive Processes

Brief description of the author's results of development of cognitive processes (CP) computer modelling concept on the basis of improving the methodology and expanding the area of using computer-based testing technology in education is suggested. The fundamental heuristics for formalizing: the concept of degree of difficulty of test tasks (TT); the degree of confidence of individual's CP concep...