Boundary value problem for the four-dimensional Gellerstedt equation

In this work, the solvability of the problem with Neumann and Dirichlet boundary conditions for the Gellerstedt equation in four variables is investigated. The energy integral method is used to prove the uniqueness of the solution to the problem. In addition to it, formulas for differentiation, autotransformation, and decomposition of hypergeometric functions are applied. The solution is obtained explicitly and is expressed by Lauricella’s hypergeometric function

Boundary value problem for the four-dimensional Gellerstedt equation

In this work, the solvability of the problem with Neumann and Dirichlet boundary conditions for the Gellerstedt equation in four variables is investigated. The energy integral method is used to prove the uniqueness of the solution to the problem. In addition to it, formulas for differentiation, autotransformation, and decomposition of hypergeometric functions are applied. The solution is obtained explicitly and is expressed by Lauricella’s hypergeometric function

Spectral properties of local and nonlocal problems for the diffusion-wave equation of fractional order

The paper investigates the issues of solvability and spectral properties of local and nonlocal problems for the fractional order diffusion-wave equation. The regular and strong solvability to problems stated in the domains, both with characteristic and non-characteristic boundaries are proved. Unambiguous solvability is established and theorems on the existence of eigenvalues or the Volterra property of the problems under consideration are proved

The Samarskii–Ionkin type problem for the fourth order parabolic equation with fractional differential operator

AbstractIn the present work the Samarskii–Ionkin type non-local problem with Caputo fractional order differential operator is studied. The considered problem generalizes some previous known problems formulated for some fourth order parabolic equations. We prove the existence and uniqueness of a regular solution of the formulated problem applying the method of separation of variables

Decomposition formulas for some quadruple hypergeometric series

In the present work, the authors obtained operator identities and decomposition formulas for second order Gauss hypergeometric series of four variables into products containing simpler hypergeometric functions. A Choi–Hasanov method based on the inverse pairs of symbolic operators is used. The obtained expansion formulas for the hypergeometric functions of four variables will allow us to study the properties of these functions. These decompositions are used to study the solvability of boundary value problems for degenerate multidimensional partial differential equations

Mathematical modeling of the source and environment response for the equation of geoelectrics

In this paper an algorithm is proposed for determining the source of excitation of electromagnetic waves emitted by the Ground - penetrating radar (GPR) device as a function of time. A mathematical model for solving this problem was constructed and tested on model data. We have built an algorithm for constructing a source function based on real georadar data. For this purpose, the results of experimental studies conducted in field conditions using the Loza-V GPR. Experiments were carried out in the medium: air - sand. The received signal of the response of the medium was processed from interference and noise. For this purpose, we use frequency filtering, signal averaging, amplitude correction for processing radarograms. In the future, the obtained table form of the disturbance signal will be used by us to study inhomogeneous media, including the study of localized objects. The series of calculations for the considered problems are given

The Samarskii–Ionkin type problem for the fourth order parabolic equation with fractional differential operator

AbstractIn the present work the Samarskii–Ionkin type non-local problem with Caputo fractional order differential operator is studied. The considered problem generalizes some previous known problems formulated for some fourth order parabolic equations. We prove the existence and uniqueness of a regular solution of the formulated problem applying the method of separation of variables