On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls

Elmira ABDILDAYEVA

In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional ...Более

Optimal distributed control for the processes of oscillation described by Fredholm integro-differential equations

Elmira ABDILDAYEVA

In this paper we investigate the problem of distributed optimal control for the oscillation processes described by Fredholm integro-differential equations with partial derivatives when the function of the external source depends nonlinearly on the control parameters. We have developed an algorithm for finding approximate solutions of nonlinear optimization problems with arbitrary precision. The developed method of solving nonlinear optimization problems is constructive and can be used in applications. - Keywords and phrases: boundary value problem, generalized solution, approximate solutions, ...Более

Polynomial Inequalities in Regions with Zero Interior Angles in the Bergman Space

Sebahattin BALCI | Meerim İmaş Kızı | Fahreddin ABDULLAYEV

We study the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space A(p)(G, h), p > 0, in regions with zero interior angles at finitely many boundary points. We obtain estimates for algebraic polynomials in bounded regions with piecewise smooth boundary.

APPROXIMATE SOLUTION OF BOUNDARY VALUE PROBLEM FOR HYPERBOLIC EQUATION WITH FREDHOLM INTEGRAL OPERATOR

Elmira ABDILDAYEVA