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On Approximate Solutions of a Nonlinear Periodic Boundary-Value Problem with Switching in the Case of Parametric Resonance by the Newton–Kantorovich Method
We study the problem of determination of conditions for the existence of solutions to weakly nonlinear periodic boundary-value problems for systems...
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On the Grad–Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations
In this work, we study the solvability of a boundary value problem for the magneto-hydrostatic equations originally proposed by Grad and Rubin...
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Weakly Perturbed Impulsive Boundary-Value Problem for Integrodifferential Systems in the Resonance Case
We establish conditions for the existence of solutions of weakly perturbed impulsive boundary-value problems for systems of integrodifferential...
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Existence and Uniqueness of the Classical Solution of the First Boundary Value Problem for Parabolic Systems on the Plane
AbstractWe consider the first boundary value problem for uniformly parabolic systems of the second order with one spatial variable in bounded and...
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Nonlinear Difference-Algebraic Boundary-Value Problem in the Case of Parametric Resonance
We determine necessary and sufficient conditions for the existence of solutions of a nonlinear boundaryvalue problem for a system of...
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Two-Point Boundary-Value Problem for Linear Stochastic Differential Equations
We present an extension of the two-point boundary problem either in the case where the problem is not always uniquely solvable or in the case where...
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On the second boundary value problem for Lagrangian mean curvature equation
Considering the second boundary value problem of the Lagrangian mean curvature equation, we obtain the existence and uniqueness of the smooth...
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Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy
AbstractWe consider the Dirichlet boundary value problem for an elliptic type equation with irregular noninteger-order degeneration in a rectangle....
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Initial–Boundary Value Problem for Flows of a Fluid with Memory in a 3D Network-Like Domain
AbstractWe consider an initial–boundary value problem for an integro-differential system that describes 3D flows of a non-Newtonian fluid with...
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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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On a general discrete boundary value problem for an elliptic pseudo-differential equation in a quadrant
We study a general discrete boundary value problem in Sobolev–Slobodetskii spaces in a plane quadrant and reduce it to a system of integral...
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On the Solvability of a Boundary Value Problem for a Two-Dimensional System of Navier–Stokes Equations in a Truncated Cone
AbstractThe paper is devoted to the problems of solvability in Sobolev classes of the boundary value problem for a two-dimensional system of...
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Three-Dimensional Initial-Boundary Value Problem for a Parabolic-Hyperbolic Equation with a Degenerate Parabolic Part
AbstractAn initial-boundary value problem is studied for a nonhomogeneous equation of mixed parabolic-hyperbolic type in three variables with a...
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The Mixed Initial-Boundary Value Problem for Degenerate Hyperbolic Equation
A new class of initial-boundary value problems with nonlocal conditions on the Newton potential for the case of a degenerate equation were set and...
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On a Method for Solving a Mixed Boundary Value Problem for a Parabolic Equation Using Modified Sinc-Approximation Operators
AbstractA new method is proposed for obtaining a generalized solution of a mixed boundary value problem for a parabolic equation with boundary...
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Monte Carlo Solution of Semi-linear Helmholtz Boundary Value Problem
In these work we will study a probabilistic representation of the solution of the Helmholtz boundary problem for the non-linear problem...
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Smooth Solution to the Second Initial-Boundary Value Problem for a Parabolic System in a Domain with Nonsmooth Lateral Boundary
We consider the second initial-boundary value problem for a Petrovskii parabolic second order system with variable coefficients in a semibounded...
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The initial-boundary value problem for a strictly hyperbolic equations
This article focuses on constructing the global solutions to initial-boundary value problem for a nonlinear strictly hyperbolic system of...
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Conditional Well-Posedness of the Initial-Boundary Value Problem for a System of Inhomogeneous Mixed Type Equations with Two Degeneration Lines
We study the conditional well-posedness of the initial-boundary value problem for a system of inhomogeneous mixed type equations with two...