Eurasian Mathematical Journal

Time optimal control problem with integral constraint for the heat transfer process

2024-04-08T06:23:19+00:00

In the present paper a mathematical model of thermocontrol processes is studied. Several convectors are installed on the disjoint subsets Г_k of the wall ∂Ω of a volume Ω and each convector produces a hot or cold flow with magnitude equal to µk(t), which are control functions, and on the surface ∂Ω \ Γ, Γ = ∪Γ_k, a heat exchange occurs by the Newton law. The control functions µ_k(t) are subjected to an integral constraint. The problem is to find control functions to transfer the state of the process to a given state. A necessary and sufficient condition is found for solvability of this problem. An equation for the optimal transfer time is found, and an optimal control function is constructed explicitly

Applications of λ-truncations to the study of local and global solvability of nonlinear equations

2024-04-08T06:35:52+00:00

In this paper, we consider the equation in a neighbourhood of a given point , where F is a given continuous mapping between finite-dimensional real spaces. We study a class of polynomial mappings and show that these polynomials satisfy certain regularity assumptions. We show that if a λ-truncation of F at ¯ belongs to the considered class of polynomial mappings then for every close to there exists a solution to the equation that is close to . For polynomial mappings satisfying the regularity conditions we study their stability to bounded continuous perturbations.

A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind

2024-04-08T07:33:38+00:00

This work is devoted to a formulation and an investigation of a boundary value problem with Gellerstedt conditions on different characteristics for the loaded parabolic-hyperbolic type equation of the second kind. By using the extremum principle and the method of energy integrals, there are proved the uniqueness of solution of the formulated problem, and the existence of a solution to the problem - by the method integral equations.

Asymptotics of the solution of parabolic problems with nonsmooth boundary functions

2024-04-08T07:39:39+00:00

In this paper, we construct the asymptotics of the solution to a singularly perturbed parabolic problem with a nonsmooth boundary layer function. In contrast to works devoted to this direction, our asymptotics contains only one boundary layer function, which is the product of parabolic and exponential boundary layer functions. Our approach allows us to construct a classical solution without applying smoothing procedures

On the associated spaces of the weighted altered cesaro space

2024-04-08T07:42:05+00:00

We study weighted altered Ces`aro space , which is a non-ideal enlargement of the usual Ces`aro space. We prove the connection of this space with one weighted Sobolev space of the first order on real line and give characterizations of associate spaces of this space.

Concinnity of dynamic inequalities designed on calculus of time scales

2024-04-08T07:46:39+00:00

We present some reverse dynamic inequalities of Radon’s and Bergstr¨om’s type on time scales in general form. The extension of Clarkson’s dynamic inequality on time scales is also given. Our further investigations explore some dynamic inequalities by using Kantorovich’s and Specht’s ratios. The calculus of time scales unifies and extends continuous results and their corresponding discrete and quantum analogues.

Porosity in the context of hypergroups

2024-04-08T07:50:55+00:00

In this paper we show that the set of all elements for which for a center element , is -c-lower porous, where is a non-compact unimodular hypergroup and B is some special symmetric compact neighborhood of the identity element. As an application, we give some new equivalent condition for the finiteness of a discrete Hermitian hypergroup. Moreover, we give some sufficient conditions for the set of all pairs in for which for a center element , is a -c-lower porous, where with . Also, we show that the complement of this set is spaceable in .

Finite groups with given systems of propermutable subgroups

2024-04-08T09:31:20+00:00

Let H be a subgroup of a finite group G. Then we say that H is propermutable in G provided G has a subgroup B such that G = NG(H)B and H permutes with all subgroups of B. In this paper, we present new properties of propermutable subgroups. Also we provide new information on the structure of a group with propermutable Sylow (Hall, maximal) subgroups and a group G = AB with propermutable subgroups A and B.