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On One Integral Representation of Solutions of Polyharmonic Equation
AbstractIn the paper, an elementary solution of polyharmonic equation is determined and, with the help of it, an integral representation of solutions...
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Mixed Problem with Integral Condition for a Loaded Third Order Pseudoparabolic Equation
We consider a nonlocal problem with an integral condition for a loaded third order pseudoparabolic equation in a rectangular domain. We prove the...
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Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures
AbstractWe consider the differential and integral statements of problems of acoustic scattering by three-dimensional bounded transparent structures...
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On a Non-Linear Differential-Integral Equation
AbstractExact analytical solutions to a non-linear differential-integral equation that appears in a stochastic optimal control problem are given. The...
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Fredholm integral equation in composed-cone metric spaces
The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples...
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Generalized Boundary Integral Equation Method for Boundary Value Problems of Two-D Isotropic Lattice Laplacian
A generalized boundary integral equation method for boundary value problems of two-dimensional isotropic lattice Laplacian is proposed in this paper....
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Uniform Aproximations of Solutions to a Strongly Singular Integral Equation of the First Kind
AbstractThe article is devoted to uniform approximations of the solution of a periodic strongly singular integral equation of the first kind. We note...
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Euler Integral Symmetries and the Asymptotics of the Monodromy for the Heun Equation
Euler integral transform connects monodromy matrices of the Heun equation with different sets of parameters. In this paper, this fact is used to...
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Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the...
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A Method for Solving the Fredholm Integral Equation of the First Kind
The paper considers a numerical method for solving the Fredholm integral equation of the first kind. The essence of the method is to replace the...
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Fredholm Integral Equation of the Second Kind with Degenerate Kernel
In this section, we will describe the method of solution of the integral equation (2.1) with degenerate kernel k(x, t) given by equation (2.4) by...
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Existence of Solutions to a Conformally Invariant Integral Equation Involving Poisson-Type Kernels
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation...
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Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space
AbstractWe study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced....
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Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition
AbstractIn this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with...
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Inverse Problems for the Helmholtz Equation on Finding the Right-Hand Side with Nonlocal Integral Observation
AbstractThe paper presents formulations of inverse problems for the Helmholtz equation on finding its right-hand side with a Samarskii–Ionkin-type...
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Accelerating the Solution of the Boltzmann Equation by Controlling Contributions to the Collision Integral
AbstractA method of reducing the number of arithmetic operations needed to evaluate the Boltzmann collision integral by the conservative projection...
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Picard Approximation of a Singular Backward Stochastic Nonlinear Volterra Integral Equation
In this paper we prove that Picard iterations of BSDEs with globally Lipschitz continuous nonlinearities converge exponentially fast to the solution....
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A Time-Nonlocal Inverse Problem for the Beam Vibration Equation with an Integral Condition
AbstractWe study the direct problem for transverse vibrations of a homogeneous beam of finite length with time-nonlocal conditions and obtain...