We consider an optimal control problem associated to Dirichlet boundary value
problem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coecients A(x) of such system as a control in L1(Ω;RN RN). One of the important features of the admissible controls is the fact that the coecient matrices A(x) are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part Asym = (A + At)=2 may vanish in Ω.
In this paper we consider an optimal control problem (OCP) for the coupled
system of a nonlinear monotone Dirichlet problem with matrix-valued L∞
(Ω;RN×N)-controls in coecients and a nonlinear equation of Hammerstein type, where solution nonlinearly depends on L∞ -control. Since problems of this type have no solutions in general, we make a special assumption on the coecients of the state equations and introduce the class of so-called solenoidal admissible controls. Using the direct method in calculus of variations, we prove the existence of an optimal control. We also study the stability of the optimal control problem with respect to the domain perturbation. In particular, we derive the sucient conditions of the Mosco-stability for the given class of OCPs.
In this paper we propose the definition algorithm of the gravitational mass of un known origin on the results of astronomical observations of the movements of other gravity bodies. Unlike a similar problem, which has been solved at first by Leverrier and J. D. Adams, in the paper a more universal algorithm was proposed. To obtain of useful estimates of the exact solutions the hypothesis was proposed, which eliminates from use the size of operator error. Conditions for the existence of estimations of exact solutions are considered. Several non-standard statements of inverse problems is investigated.
New exact solution of the spherically-axissymmetric Eilers equations, called as planetary vortex, is applied to the problem of formation in planetary nebula germs of planets due to the condensation of gases in the areas of vortex instability which calls the rings of planetary vortex. It is shown that the vortex perturbations causes changes in preassure and temperature at which the gases of nebula condense themselves, forming the germs of the planets.
A comparative study of two fundamental solutions of the space-axisymmetric Euler equations, one of which is regular throughout space and describes the regular system of vortex rings, and the other is singular at the origin. It is shown that despite the feature zero singular solution generates a flow with finite integral characteristics of vortex rings and systems similar to a regular case and close to it on the global structure.
One class of optimal control problems for degenerate parabolic equation with Dirich-let boundary conditions and a priori feedback law are considered. It is shown that such problems have an optimal solution in the corresponding weighted Sobolev space provided the operators of feedback laws possess special compactness properties.
We study one class of nonlinear fluid dynamic models with controls in the initial condition and the source term. The model is described by a nonlinear inhomogeneous hyperbolic conservation law with state and control constraints. We apply the so-called vector-valued approximation of the original optimal vector problem. Conditions under which the solutions to approximation problems will be admissible for the original problem are derived.
Constructed and substantiated refined mathematical model of multiple-rope hoist. The dynamic processes that occur in the main rope, with the aim to improve the strength and durability of lifting and balancing ropes. The results of calculations.
The necessary optimality conditions to optimal control problem for parabolic system with unbounded coefficients were developed using the concept of the generalized right hand directional derivative and quasi-adjoint state.
The analytical solution for heating of the layer of massive bodies regular shape, that located in a moving gas stream, has developed. Uniform procedure for calculating the number of members in a solution is proposed, that allows calculations with an arbitrary number of terms in the expansion. Effectiveness of the procedure is shown in the example of solving the problem of unsteady heat transfer in a moving bed of spherical particles.