Bitsadze Samarskii Research Articles

On an inverse problem of the Bitsadze–Samarskii type for a parabolic equation of fractional order

On an inverse problem of the Bitsadze–Samarskii type for a parabolic equation of fractional order

Bitsadze–Samarskii Type Problem for a Mixed Type Equation That is Elliptic in the First Quadrant of the Plane

Bitsadze–Samarskii Type Problem for a Mixed Type Equation That is Elliptic in the First Quadrant of the Plane

Inverse Problem of Bitsadze–Samarskii Type for a Two-Dimensional Parabolic Equation of Fractional Order

Inverse Problem of Bitsadze–Samarskii Type for a Two-Dimensional Parabolic Equation of Fractional Order

Inverse Nodal Problem for a Conformable Fractional Diffusion Operator With Parameter-Dependent Nonlocal Boundary Condition

In this paper, we consider the inverse nodal problem for the conformable fractional diffusion operator with parameter-dependent Bitsadze–Samarskii type nonlocal boundary condition. We obtain the asymptotics for the eigenvalues, the eigenfunctions, and the zeros of the eigenfunctions (called nodal points or nodes) of the considered operator, and provide a constructive procedure for solving the inverse nodal problem, i.e., we reconstruct the potential functions p(x) and q(x) by using a dense subset of the nodal points.

On a Spectral Problem for the Cauchy–Riemann Operator with Boundary Conditions of the Bitsadze–Samarskii Type

On a Spectral Problem for the Cauchy–Riemann Operator with Boundary Conditions of the Bitsadze–Samarskii Type

On a semilinear parabolic problem with non-local (Bitsadze–Samarskii type) boundary conditions in more dimensions

This paper studies a semilinear parabolic equation in a bounded domain Ω⊂Rd along with nonlocal boundary conditions. The boundary values are linked to the values of a solution on an interior (d−1)-dimensional manifold lying inside Ω. Firstly, the solvability of a steady-state problem is addressed. Secondly, involving the semi-discretization in time, a constructive algorithm for approximation of a solution to a transient problem is developed. The well-posedness of the problem in a weighted Hilbert space is shown. Convergence of approximations is addressed and the error estimated are derived. Numerical experiments support the theoretical algorithms.

On Periodic Solutions of Quasilinear Parabolic Equations with Boundary Conditions of Bitsadze–Samarskii Type

On Periodic Solutions of Quasilinear Parabolic Equations with Boundary Conditions of Bitsadze–Samarskii Type

Problem with a Bitsadze–Samarskii Condition on Parallel Characteristics for a Mixed Type Equation of the Second Kind

Problem with a Bitsadze–Samarskii Condition on Parallel Characteristics for a Mixed Type Equation of the Second Kind

ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND EIGENFUNCTIONS OF A NONLOCAL BOUNDARY VALUE PROBLEM

In this work, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the second order boundary-value problem with a Bitsadze–Samarskii type nonlocal boundary condition.

On general Bitsadze–Samarskii problems of elliptic type in $$L^{p}$$ cases

On general Bitsadze–Samarskii problems of elliptic type in $$L^{p}$$ cases

Unique Solvability of Problems for a Mixed Parabolic Equation in Unbounded Domain

In the work, parabolic equations with perpendicular time directions considered together and the Gevrey problem with generalized gluing conditions, and a problem with the Bitsadze–Samarskii conditions have been studied. The uniqueness and existence of the solution of the considered problems were proved. The Gevrey problem was equivalently reduced to the two-point problem for ordinary differential equation involving fractional differential operators. The uniqueness of the solution of the obtained problem was proved by the principle of extremum and the existence was proved by the method of integral equations. The theory of the second kind Volterra integral equations and properties of two-parameter Mittag-Leffler function are applied at studying a unique solvability of the problem with Bitsadze–Samarskii condition. Necessary conditions for given functions for solvability of considered problems have been found.

The Bitsadze–Samarskii Type Problem for Mixed Type Equation in the Domain with the Deviation from the Characteristics

For a mixed elliptic-hyperbolic type equation in a mixed domain, when the elliptic part is a sector of the circle, and the hyperbolic part consists of two characteristic triangles, the Bitsadze–Samarskii type nonlocal problem is investigated. A feature of such problems is that the boundary conditions in the hyperbolic parts of the boundary are determined by a first-order differential operator and pointwise link the values of the partial derivatives of the desired solution on the characteristics with the partial derivatives on arbitrary monotone curves lying inside the characteristic triangles of the equation. To solve the problem, the methods of the theory of partial differential equations and the theory of singular integral equations as well as the methods of energy integrals and complex analysis were used, with the help of which the existence and uniqueness theorem for the solution of the investigated problem is proved. Also, a method of reducing the investigated problem to an equivalent system of singular integral equations is shown, also, a method for solving this system is proposed, which allows to obtain a solution to the problem in explicit form.

Bitsadze–Samarskii Boundary Conditions for an Elliptic-Parabolic Volume Potential with Smooth Matching

Bitsadze–Samarskii boundary conditions are obtained for a regular elliptic-parabolic volume potential given in a cylindrical domain based on the spectral decomposition of Green’s function of the Holmgren problem.

Bitsadze–Samarskii type problem for the integro-differential diffusion–wave equation on the Heisenberg group

This paper deals with the fractional generalization of the integro-differential diffusion–wave equation for the Heisenberg sub-Laplacian, with homogeneous Bitsadze–Samarskii type time-nonlocal conditions. For the considered problem, we show the existence, uniqueness and the explicit representation formulae for the solution.

Bitsadze–Samarskii problem for parabolic systems with Dini continuous coefficients

ABSTRACTWe consider a nonlocal initial-boundary value problem of the Bitsadze–Samarskii type for spatially one-dimensional parabolic second-order systems with Dini continuous coefficients in a domain with nonsmooth lateral boundaries. By the boundary integral equations method we construct a classical solution of this problem. The smoothness of the solution is studied.

Bitsadze–Samarskii Boundary Condition for Elliptic-Parabolic Volume Potential

A spectral decomposition of the Green’s function of the Holmgren problem in a cylindrical domain is used to obtain Bitsadze–Samarskii boundary conditions for a regular elliptic-parabolic volume potential.

Antrosios eilės diferencialinio uždavinio su viena nelokaliąja sąlyga minimalusis sprendinys

In this paper, we investigate the minimizer of the residual for the second order differential problem with one initial and other nonlocal Bitsadze–Samarskii condition. We obtain the representation of the minimizer and present an example.

Solution of the Bitsadze–Samarskii problem for a parabolic system in a semibounded domain

We consider a nonlocal initial–boundary value Bitsadze–Samarskii problem for a spatially one-dimensional parabolic second-order system in a semibounded domain with nonsmooth lateral boundary. The boundary integral equation method is used to construct a classical solution of this problem under the condition that the vector function on the right-hand side in the nonlocal boundary condition only has a continuous derivative of order 1/2 vanishing at t = 0. The smoothness of the solution is studied.

An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems

Abstract In this paper, an iterative method is proposed to solve the nonlinear Bitsadze–Samarskii boundary value problems with multi-point boundary conditions. The algorithm is based on the reproducing kernel Hilbert space method. We use an iterative scheme to overcome the nonlinearity of the problem. The convergence and error estimate of the iterative scheme are established. The reproducing kernel Hilbert space method is used to generate an approximation of the linearized problem. In fact, the reproducing kernel Hilbert space method is combined with an iterative scheme to approximate the solution and an error estimate of the approximate solution is derived. In order to show the efficiency and versatility of the proposed method, some numerical results are reported. The comparison of numerical results with the analytical solution and the best results reported in the literature confirms the good accuracy and applicability of the proposed method.

Well-Posedness of a Fourth Order of Accuracy Difference Scheme for Bitsadze–Samarskii-Type Problem

ABSTRACTIn the present study, a fourth order of accuracy difference scheme for the approximate solution of the Bitsadze–Samarskii type nonlocal boundary value problem with the integral condition is investigated. Theorem on well-posedness of the difference scheme in the difference analogue of Hölder spaces with a weight is established. In applications, coercive stability estimates for the solutions of difference schemes of nonlocal boundary value problems for elliptic problems are obtained.