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Endogenous Boundary Value Problems
Continuing the unified approach, we will first solve abstract equations involving a maximal operator of differential quadruplets. Next these...
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Higher-Order Finite-Difference Schemes for Nonlinear Two-Point Boundary Value Problems
We present a family of high-order multi-point finite difference methods for solving nonlinear two-point boundary value problems. The family involves...
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Asymptotics of the Solution of an Initial–Boundary Value Problem for the One-Dimensional Klein–Gordon Equation on the Half-Line
AbstractThe initial–boundary value problem for the Klein–Gordon equation on the half-line is considered. It is possible to reduce to this problem...
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Some Boundary-Value Problems of Fractional Differential Filtration Dynamics Regarding the Biparabolic Mathematical Model
Closed-form solutions are obtained to some one-dimensional boundary-value problems of modeling anomalous filtration dynamics in a layered geoporous...
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Linear Boundary-Value Problems for Systems of Integrodifferential Equations with Degenerate Kernel. Resonance Case for a Weakly Perturbed Boundary-Value problem
We consider a noncritical case for linear boundary-value problems posed for systems of integrodifferential equations. We establish the existence...
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Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions
This work, which can be considered as a small monograph, is devoted to the study of two-and three-dimensional boundary-value problems for eigenvalues...
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Nonstandard Boundary Value Problems of Theory of Two-Dimensional Vector Fields
We study nonstandard boundary value problems of field theory for the system of Poisson equations. The feature of these problems is that the solution...
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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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Discrete Equations, Discrete Transformations, and Discrete Boundary Value Problems
AbstractWe study the solvability of discrete elliptic pseudodifferential equations in a sector of the plane. Using special factorization of the...
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Transmutation Operators Based on Homotope Analysis for Nonlocal Boundary Value Problems
AbstractTransmutation operators nonlocal boundary value problems in terms of the homotopic analysis method is used to solve and research nonlocal...
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One-Dimensional Variational Problems
This chapter is devoted to one of the most classical classes of variational problems, the one-dimensional case.
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The solvability of inhomogeneous boundary-value problems in Sobolev spaces
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary...
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Schemes of Finite Element Method for Solving Multidimensional Boundary Value Problems
We propose new computational schemes and algorithms of the finite element method for solving elliptic multidimensional boundary value problems with...
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The Models of Gradient Mechanics and Singularly Perturbed Boundary Value Problems
AbstractModels of gradient mechanics are presented and asymptotic methods for solving singularly perturbed boundary value problems of gradient...
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Boundary-Value Problems for Differential Systems with Pulsed Action
We establish the coefficient necessary and sufficient conditions for the existence of solutions of weakly nonlinear boundary-value problems for...
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Triple Mixed Integral Transformation and Applications for Initial-Boundary Value Problems
In this paper, we establish a new integral transformation method for solving the initial-boundary value problems of the partial differential...
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Boundary value problems of quaternion-valued differential equations: solvability and Green’s function
This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential...
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On some even-sequential fractional boundary-value problems
In this paper we provide a way to handle some symmetric fractional boundary-value problems. Indeed, first, we consider some system of fractional...
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Linear inverse problems for the heat equation and non-local boundary value problems with generalized Samarskii–Ionkin condition
The paper is devoted to the study of the solvability of linear inverse problems for a one-dimensional heat equation with an unknown right-hand side....