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Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition
AbstractWe consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion...
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Numerical Solution of the Boundary Value Problem for Internal Inertia-Gravity Waves
AbstractThe initial and boundary value problem for the equations of free internal inertia-gravity waves in an unconfined basin of constant depth is...
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On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations
AbstractFor a system of nonlinear integral equations on the semiaxis, we study a boundary value problem whose matrix kernel has unit spectral...
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Initial Boundary Value Problems
This chapter first discusses the initial boundary value problems in the advection and diffusion equations. The corresponding schemes to deal with the...
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Asymptotic Behavior Associated with the Definition of One Boundary Value Problem for the Laplace Equation
AbstractThe eigenvalues of one boundary value problem for the Laplace equation are studied. Asymptotic formulas for the eigenvalues are found.
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Asymptotics of the Solution of the Initial Boundary Value Problem for the One-Dimensional Klein–Gordon Equation with Variable Coefficients
AbstractIn the paper, formal asymptotic solutions of the initial-boundary value problem for the one-dimensional Klein–Gordon equation with variable...
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Mathematical Boundary Value Problem of Linear Electro-Elasticity
In this chapter, we present the formulation of the mathematical boundary value problem of linear electro elasticity. Based on the rules for the...
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On One Nonlinear Inverse Boundary Value Problem for Linearized Sixth-Order Boussinesq Equation with an Additional Integral Condition
AbstractA huge number of mathematical models are called Boussinesq-type equations; therefore, a wide range of sixth-order Boussinesq-type equations...
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Boundary Value Problems and Solutions
In the previous chapters we have used the complete integrability of the stationary axisymmetric Einstein equations in vacuum to construct and to...
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Sturm-Liouville Boundary Value Problem for a Sea-Breeze Flow
We present recent results in study of a mathematical model of the Sea-Breeze flow, arising from a general model of the ‘morning glory’ phenomena....
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Exact Solutions to Inhomogeneous Boundary Value Problems of the Theory of Elasticity in a Rectangle
AbstractA method is proposed for building exact solutions to boundary value problems of the theory of elasticity in a rectangle with stiffeners...
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Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts
AbstractBoundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift...
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DISCRETE METHOD FOR SOLVING A THREE-POINT BOUNDARY-VALUE PROBLEM FOR A THIRD-ORDER EQUATION
AbstractAdjoined equations are used to develop a method for solving boundary-value problems for second- and third-order equations. With the use of...
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Some new methods for studying boundary value problems for general partial differential equations
AbstractWe consider methods for studying boundary value problems for linear partial differential equations in a domain regardless of the type of...
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The Initial Boundary Value Problem for the Einstein Equations with Totally Geodesic Timelike Boundary
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the...
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Boundary Value Problems for Parabolic Equations in Noncylindrical Domains
AbstractA mathematical theory is developed for constructing integral relations of a new type in analytical solutions of boundary value problems for...
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Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity
Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the...
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Spatially One-Dimensional Boundary Value Problems of Coupled Thermoelasticity: Generalized Functions Method
AbstractProblems of determining the thermostressed state of a thermoelastic rod using the coupled thermoelasticity model are considered. In this...
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Highly Accurate Numerical Schemes for Solving Plane Boundary-Value Problems for a Polyharmonic Equation and Their Application to Problems of Hydrodynamics
AbstractBoundary-value problems are considered for harmonic and biharmonic equations, as well as the general polyharmonic equation for multiply...
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Sticky Brownian Motions and a Probabilistic Solution to a Two-Point Boundary Value Problem
In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which...