Boundary integral representation for the linear Beltrami vector fields are obtained. It is marked that the given integral equations allow the effective numerical solving. Shown that in the case boundary value problem of the first kind solution can be obtained by quadratures.
We discuss the existence of weak solutions to the Cauchy problem for one class
of hyperbolic conservation laws that models a highly re-entrant production system.
The output of the factory is described as a function of the work in progress and the
position of the so-called push-pull point (PPP) where we separate the beginning of
the factory employing a push policy from the end of the factory, which uses a pull
policy. The main question we discuss in this paper is about the optimal choice of
the input in-ux, push and pull constituents, and the position of PPP.
We study a Dirichlet optimal control problem for a quasilinear monotone p-Laplace equation with control and state constraints. The coefficient of the p-Laplacian, the weight u, we take as a control in L1(Ω). We discuss a relaxation of such problem following the so-called Henig regularization scheme.
Some generalizations of a method of nonlocal transformations are proposed: a connection of given equations via prolonged nonlocal transformations and finding of an adjoint solution to the solutions of initial equation are considered. A concept of nonlocal transformation with additional variables is introduced, developed and used for searching symmetries of differential equations. A problem of inversion of the nonlocal transformation with additional variables is investigated and in some cases solved. Several examples are presented. Derived technique is applied for construction of the algorithms and formulae of generation of solutions. The formulae derived are used for construction of exact solutions of some nonlinear equations.
We study a Dirichlet optimal control problem for biharmonic equation with
control and state constraints. The coecient of the biharmonic operator, the weight
u, we take as a control in L1(Ω). We discuss the relaxation approach and show that
some optimal solutions to the original problem can be attained in the limit by
optimal solutions of some extremal problem for variational inequality with a special
penalized cost functional.
The algorithm for parameter identification of adequate mathematical model in algebraic form is examinated. The definition of an adequate mathematical model in algebraic form is given. In article the several formulations of the problems of identification depending on the ultimate goals of the study is proposed. As an example, the problem of identifying the parameters of algebraic adequate mathematical model of conditionally stable process of steelmaking is considered. The results can be used to analyze the influence of the physical parameters to the physical process.
This work is devoted to the study of some one-dimensional dynamical systems with discrete time, for which rounding to the different number of decimal places leads to the qualitative change in orbits. It is proved that the behavior of the trajectories of dynamical systems essentially depends on the order of rounding.
The theory of planetary vortex as the initial state of creation of the star systems is used to the study of conditions of formation of asteroids and calculation its orbital parameters. In application to Main asteroid belt of the Solar system the kind coincidence of theoretical and experimental data is got.
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