Conditions of Existense and Uniqueness of Solutions of Parabola-Hyperbolic Equation with Nonolocal Boundary Conditions

Processes described with parabola-hyperbolic differential equations are crucial in the theory of mathematical physics. The article deals with the heterogeneous parabola-hyperbolic equation with nonlocal boundary conditions. To further investigate this class of problems, we need to find its classical solution. We show the system of eigenfunctions and associated functions of the boundary value problem.

Optimal Control for Singular Perturbed Periodic Parabolic Equations with Nonlocal Boundary Value Conditions

This paper considers the issues of optimal control for singular perturbed by the spatial value linear parabolic equations with nonlocal boundary value conditions and the quadratic performance criterion. We construct the complete asymptotes of optimal solutions for the initial problem under optimal conditions by boundary functions method. Unlike similar problems for parabolic equations with local boundary value conditions, the iterative problems for boundary functions do not “decompose”.

Solutions properties for one class of parameterized operator inclusions

This paper provides the insights into the properties of solutions for parameterized operator inclusions with multi-valued maps of type. We prove the resolvability of such inclusions, weak compactness and parameter dependence of their solution. Moreover, we provide the example, illustrating the obtained results.

The sufficient conditions of the shape stability for perturbation of the one class of optimal control problems

We address the optimal control problems in the coefficients for a nonlinear elliptic equation with Dirichlet boundary conditions for generalized solenoidal controls. We define the shape stability concept for optimal control problems. Finally, we reveal the sufficient conditions for perturbation of the domain, under which the shape stability of the problem under study occurs.

Advertising activity optimization of the insurance company from a position of the guaranteed gain

This paper proposes the model of the insurance company activity, which calculates the publicity expenses insurance services. We illustrate that the obtained algorithm allows to calculate the final guaranteed gain of the company on a given set of the insurance firm initial data.

The investigation of a model of spontaneous market economy with diffusion of operating parameters and control function

Using Weidlich’s approach to the interaction of operating parameters, we study the behavior of a dynamical model with a chaotic behavior. Furthermore, we introduce the control function to stabilize national economy.