The paper is devoted to the study of the problem of identifying a coefficient in the right-hand side of a one-dimensional third-order hyperbolic equation known as the Moore–Gibson–Thompson (MGT) equation with Dirichlet boundary conditions. An integral overdetermination condition serves as additional information required to recover the coefficient. The main goal of the work is to prove the existence of a solution in Sobolev spaces. The proof method is based on reducing the original inverse problem to an auxiliary direct problem. The solvability of the auxiliary problem is established using the parameter continuation method and the regularization method. A key step is obtaining a priori estimates for solutions in specially introduced function spaces. The paper formulates sufficient conditions on the problem’s input data that guarantee the existence of solution to the direct problem. The solution to the inverse problem is then explicitly expressed through the solution of the direct problem.

The paper investigates the optimal control problem for a stochastic model of nonlinear filtering with a random initial value. Since random interference occurs at the initial moment of time, the solution to the problem is sought as a sum of deterministic and stochastic components. This feature allows us to study the initial problem based on the study of two problems: the optimal control problem for solutions of a deterministic equation with the Showalter–Sidorov–Dirichlet condition and the Showalter–Sidorov– Dirichlet problem for an inhomogeneous stochastic equation.

The paper considers a second-order elliptic equation in a bounded plane domain whose principal operator is the Laplace operator with a strong polar singularity in the lowest coefficient. The construction of an integral representation for the general solution is explored, as well as its application to the study of boundary value problems.

Queuing systems (QS) are analytical models of information networks and their individual elements. In this paper we consider a QS with infinite storage capacity, one server, and exponential service with intensity µ. The input of the QS is a doubly stochastic Poisson flow of customers with diffusion rate λ(t) ∈ [α, β] with elastic borders. The diffusion process λ(t) has zero drift coefficient a = 0 and diffusion coefficient b > 0. Moments of unfinished work are found in the stationary mode. A necessary condition for the existence and uniqueness of a stationary mode in a broad sense in a QS is obtained from the unfinished work.

We study the equilibrium problem for a hyperelastic body containing a crack that crosses the boundary at zero angle. First, we consider the case where the crack and the boundary form a regular cusp. The problem is formulated as minimization of an energy functional over a set of admissible deformations and we prove an existence theorem. Then we address the general case of an irregular cusp. For this case, we develop an approach based on the fictitious domain method, which allows us to relax the restrictive geometric assumptions on the cusp sharpness and to prove an existence theorem for the corresponding variational problem.

We define two new BMOA type analytic function spaces in polydisk. We provide many new results concerning coefficient multipliers of these two new BMOA analytic function spaces in polydisc. Our results extend previously known assertions obtained by various authors. Our results extend certain previously known theorems on coefficient multipliers on BMOA type spaces obtained by M. Pavlovic and M. Mateljevic and M. Jevtic and others in the unit disk to the case of several complex variables. Our research on coefficient multipliers of analytic spaces of several complex variables can be viewed by experts as new research area, our assertions may be applied to various problems in complex function theory of several variables.

This paper presents a new class of contact problems between solids having wedge shaped edges, focusing on the analysis of contact problems in three dimensions defined over a non-convex admissible set. Specifically, contact between a composite body and a rigid obstacle is studied, where the composite consists of an elastic matrix and an incorporated rigid inclusion interacting with an obstacle. A system of inequality type conditions for displacements ensuring non-penetration of solid points is derived. According to the system of restrictions, the set of admissible displacements is provided. The existence of a solution to an energy minimization problem over the admissible set is established. For particular cases of considered contact problems corresponding differential formulations are derived. The main result of this study lays the foundation for a new type of mathematical model for contact problems involving three-dimensional composite materials.

This paper presents a one-dimensional steady-state mathematical model describing the transport of organic pollution in a river. The model incorporates the key physical and chemical processes: advection, diffusion, biochemical oxidation of pollutants accompanied by the consumption of dissolved oxygen, and natural surface reaeration. The boundary-value problem for the system of nonlinear ordinary differential equations is solved numerically using the MATLAB environment. A computational experiment is carried out to analyze the dynamics of pollutant concentration and dissolved oxygen along the studied river reach under various pollutant discharge scenarios.