共查询到20条相似文献,搜索用时 31 毫秒
1.
Olaf Post 《Mathematische Nachrichten》2016,289(8-9):1052-1099
We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define abstract Neumann and Dirichlet boundary conditions and a corresponding Dirichlet‐to‐Neumann operator, and develop a theory relating resolvents and spectra of these operators. We illustrate the theory by many examples including Jacobi operators, Laplacians on spaces with (non‐smooth) boundary, the Zaremba (mixed boundary conditions) problem and discrete Laplacians. 相似文献
2.
We consider an initial-boundary value problem for the one-dimensional nonstationary Schr?dinger equation on the half-axis
and study a two-level symmetric finite-difference scheme of Numerov type with higher approximation order. This scheme is constructed
on a finite mesh, which is uniform with respect to space, with a nonlocal approximate transparent boundary condition of a
general form (of Dirichlet-to-Neumann type). We obtain assertions about the stability of the finite-difference scheme in two
norms with respect to the initial data and free terms in the equation and in the approximate transparent boundary condition
under suitable conditions in the form of inequalities on the operator of approximate transparent boundary condition. Bibliography:
12 titles. 相似文献
3.
V. S. Gavrilov 《Differential Equations》2016,52(8):1011-1022
We prove the existence and uniqueness of an energy class solution of an initial–boundary value problem for a semilinear equation in divergence form. We consider the case in which an inhomogeneous third boundary condition is posed on one part of the lateral surface of the cylinder in which the equation is studied and the homogeneous Dirichlet boundary condition is posed on the other part of the lateral surface. 相似文献
4.
In connection with the theory for Brownian motion on fractals, a corresponding Dirichlet form has been defined. We consider here the fractal known as the Sierpinski gasket, and characterize the trace of the domain of the Dirichlet form to the boundary of the gasket, boundary in this context meaning the triangle which confines the gasket. 相似文献
5.
We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. Our main goal is construct the Green function for the operator with mixed boundary conditions in a Lipschitz domain. Thus we specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We require a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary conditions. Our proof proceeds by defining a variant of the space BMO(Ω) that is adapted to the boundary conditions and showing that the solution exists in this space. We also give a construction of the Green function with Neumann boundary conditions and the fundamental solution in the plane. 相似文献
6.
L. A. Alexeyeva 《Differential Equations》2010,46(4):515-522
We consider boundary value problems for an elastic medium bounded by a cylindrical surface on which a load with a constant-in-time
form is moving at a constant subsonic velocity. This class of problems is a model class for the dynamics of underground structures
like transport tunnels and ground transport. The method of generalized functions is developed for the solution of boundary
value problems. We construct dynamic analogs of Green formulas and use them to derive singular boundary integral equations,
which solve the considered boundary value problems. 相似文献
7.
Dagmar Medková 《Numerical Algorithms》2010,54(4):459-484
The Neumann problem for the Stokes system is studied on a domain in R
3 with Ljapunov bounded boundary. We construct a solution of this problem in the form of appropriate potentials and determine
unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in
the form of a series. 相似文献
8.
We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self‐adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self‐adjoint operators. We then characterize the lower bounded self‐adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions. 相似文献
9.
E. I. Moiseev 《Differential Equations》2011,47(11):1675-1679
We consider the optimal boundary control of string vibrations and study the case of boundary force control at one end of the
string, the other end being free. We show that if the initial and terminal data are arbitrary, then the dependence of the
optimal boundary control on these data may be nonlinear. Conditions under which the dependence is linear are indicated. An
example is considered in which the optimal control can be found in closed form. 相似文献
10.
We consider a boundary value problem for the stationary diffusion equation outside cuts on the plane. The Dirichlet condition is posed on one side of each cut, and an oblique derivative condition is posed on the other side. We prove existence and uniqueness theorems for the solution of the boundary value problem. We obtain an integral representation of a solution in the form of potentials. The densities of these potentials are found from a system of Fredholm integral equations of the second kind, which is uniquely solvable. We obtain closed asymptotic formulas for the gradient of the solution of the boundary value problem at the endpoints of the cuts. 相似文献
11.
We find the general solution of the reflection equation associated with the Jordanian deformation of the SL(2)-invariant Yang
R-matrix. A special scaling limit of the XXZ model with general boundary conditions leads to the same K-matrix. Following
the Sklyanin formalism, we derive the Hamiltonian with the boundary terms in explicit form. We also discuss the structure
of the spectrum of the deformed XXX model and its dependence on the boundary conditions. 相似文献
12.
T. B. Solomyak 《Journal of Mathematical Sciences》1994,72(6):3459-3466
We consider a planar domain, namely a curvilinear quadrilateral. We study a variational inequality of special form on the set of functions that are monotonically increasing on part of the boundary. This problem corresponds to a one-sided problem for an elliptic equation. A boundary condition of first kind is prescribed on part of the boundary, while on the other part of the boundary the tangential derivative is nonnegative and the product of the tangential and oblique derivatives is zero. We establish that the first derivatives of the solution satisfy a Hölder condition. Bibliography: 5 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 173–186. 相似文献
13.
V. V. Solov’ev 《Differential Equations》2013,49(8):996-1005
We study sufficient conditions for the unique solvability of the inverse coefficient problem. We obtain various global sufficient conditions in the form of constraints on the signs of the given functions and their derivatives. As a corollary, we consider statements of inverse coefficient problems with overdetermination on the boundary, where the Dirichlet conditions are supplemented with the vanishing condition for the normal derivative on part of the boundary. 相似文献
14.
We consider partial regularity for energy minimizing maps satisfying a partially free boundary condition. This condition takes
the form of the requirement that a relatively open subset of the boundary of the domain manifold be mapped into a closed submanifold
with non-empty boundary, contained in the target manifold. We obtain an optimal estimate on the Hausdorff dimension of the
singular set of such a map. Our result can be interpreted as regularity result for a vector-valued Signorini, or thin-obstacle,
problem. 相似文献
15.
A. S. Minenko 《Ukrainian Mathematical Journal》1998,50(12):1929-1938
We prove the solvability of a boundary-value problem in the case where the Bernoulli condition is given on a free boundary
in the form of an inequality. We establish the analyticity of the free boundary.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1692–1700, December, 1998. 相似文献
16.
I. A. Chernov 《Differential Equations》2010,46(7):1053-1062
We consider a nonlinear parabolic boundary value problem of the Stefan type with one space variable, which generalizes the
model of hydride formation under constant conditions. We suggest a grid method for constructing approximations to the unknown
boundary and to the concentration distribution. We prove the uniform convergence of the interpolation approximations to a
classical solution of the boundary value problem. (The boundary is smooth, and the concentration distribution has the necessary
derivatives.) Thus, we prove the theorem on the existence of a solution, and the proof is given in constructive form: the
suggested convergent grid method can be used for numerical experiments. 相似文献
17.
We consider the American option pricing problem in the case where the underlying asset follows a jump‐diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro‐partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary. 相似文献
18.
《Quaestiones Mathematicae》2013,36(4):305-328
Abstract We consider the regularity up to the boundary of solutions of those elliptic boundary value problems that can be treated by the non-variational theory developed by Schechter and others. The usual method of differential quotients is replaced by a method of Schappel [5] which is based on the properties of a Laplace-type operator 1-?2. In this paper the results of Schappel, which are given for boundary value problems in variational form, are extended to the non-variational case. We make important use of fractional order Sobolev spaces on the boundary and trace theorems. 相似文献
19.
A. Aimi M. DiligentiC. Guardasoni 《Journal of Computational and Applied Mathematics》2011,235(7):1746-1754
We consider two-dimensional interior wave propagation problems with vanishing initial and mixed boundary conditions, reformulated as a system of two boundary integral equations with retarded potential. These latter are then set in a weak form, based on a natural energy identity satisfied by the solution of the differential problem, and discretized by the related energetic Galerkin boundary element method. Numerical results are presented and discussed. 相似文献
20.
V. V. Solov’ev 《Differential Equations》2013,49(12):1560-1568
We study sufficient conditions for the unique solvability of the inverse coefficient problem. We obtain various global sufficient conditions in the form of constraints on the signs of the given functions and their derivatives. As a corollary, we consider statements of inverse coefficient problems with overdetermination on the boundary, where the Dirichlet conditions are supplemented with the vanishing condition for the normal derivative on part of the boundary. We prove sufficient conditions for the existence of a solution in this case. 相似文献