共查询到20条相似文献,搜索用时 44 毫秒
1.
A. M. Akhtyamov 《Differential Equations》2017,53(11):1515-1518
We describe all degenerate two-point boundary conditions possible in a homogeneous spectral problem for the diffusion operator. We show that the case in which the characteristic determinant is identically zero is impossible for the nonsymmetric diffusion operator and that the only possible degenerate boundary conditions are the Cauchy conditions. For the symmetric diffusion operator, the characteristic determinant is zero if and only if the boundary conditions are falsely periodic boundary conditions; the characteristic determinant is identically a nonzero constant if and only if the boundary conditions are generalized Cauchy conditions. 相似文献
2.
In a Hilbert space H, we study the Fredholm property of a boundary value problem for a fourth-order differential-operator equation of elliptic type with unbounded operators in the boundary conditions. We find sufficient conditions on the operators in the boundary conditions for the problem to be Fredholm. We give applications of the abstract results to boundary value problems for fourth-order elliptic partial differential equations in nonsmooth domains. 相似文献
3.
Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equation. In turn this application gives the idea of introducing a layer close to the truncation boundary which leads to a new way of optimizing absorbing boundary conditions for truncating domains. We optimize the conditions in the case of straight boundaries and illustrate our analysis with numerical experiments both for truncating domains and the Schwarz waveform relaxation algorithm.
4.
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
5.
In the framework of the zeta-regularization approach, we consider the polarization of the scalar field vacuum with nontrivial
boundary conditions originating from electrodynamics in the presence of a conducting infinitely thin boundary layer. Boundary
conditions of the first type correspond to the case where the field is continuous on the boundary while its derivative has
a jump proportional to the boundary value of the field. Boundary conditions of the second type correspond to the case where
the field derivative is continuous on the boundary but the field itself has a jump proportional to the field derivative on
the boundary. We explicitly obtain the zeta function of the scalar field Laplace operator with the above boundary conditions
and calculate all the heat kernel coefficients. We obtain an expression for the energy of the scalar field vacuum fluctuations. 相似文献
6.
Gleiciane da Silva Aragão Sergio Muniz Oliva 《Journal of Differential Equations》2012,253(9):2573-2592
In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction–diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter ? goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. 相似文献
7.
Canonical forms of boundary conditions are important in the study
of the eigenvalues of boundary conditions and their numerical
computations. The known canonical forms for self-adjoint differential
operators, with eigenvalue parameter dependent boundary conditions,
are limited to 4-th order differential operators. We derive
canonical forms for self-adjoint $2n$-th order differential
operators with eigenvalue parameter dependent boundary conditions.
We compare the 4-th order canonical forms to the canonical forms
derived in this article. 相似文献
8.
Matthew D. Blair Hart F. Smith Christopher D. Sogge 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1817-1829
We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcritical case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions. 相似文献
9.
The conventional way of constructing boundary functions for wavelets on a finite interval is by forming linear combinations of boundary-crossing scaling functions. Desirable properties such as regularity (i.e. continuity and approximation order) are easy to derive from corresponding properties of the interior scaling functions. In this article we focus instead on boundary functions defined by recursion relations. We show that the number of boundary functions is uniquely determined, and derive conditions for determining regularity from the recursion coefficients. We show that there are regular boundary functions which are not linear combinations of shifts of the underlying scaling functions. 相似文献
10.
C. Besse M. Ehrhardt I. Lacroix‐Violet 《Numerical Methods for Partial Differential Equations》2016,32(5):1455-1484
We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455–1484, 2016 相似文献
11.
We consider a three-dimensional boundary value problem for the Laplace equation on a thin plane screen with boundary conditions for the “directional derivative”: boundary conditions for the derivative of the unknown function in the directions of vector fields defined on the screen surface are posed on each side of the screen. We study the case in which the direction of these vector fields is close to the direction of the normal to the screen surface. This problem can be reduced to a system of two boundary integral equations with singular and hypersingular integrals treated in the sense of the Hadamard finite value. The resulting integral equations are characterized by the presence of integral-free terms that contain the surface gradient of one of the unknown functions. We prove the unique solvability of this system of integral equations and the existence of a solution of the considered boundary value problem and its uniqueness under certain assumptions. 相似文献
12.
13.
Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. We develop a new method for computing the interface conditions in terms of the index of boundary value problems in weighted spaces on infinite cones, combined with structures from the calculus of boundary value problems on a manifold with edges. This will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator. The approach itself is completely general. 相似文献
14.
In this paper, we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls, and make a deep discussion on it. We analyze the relation-ship between the partial approximate boundary synchronization and the partial exact boundary synchronization, and obtain sufficient conditions to realize the partial approximate boundary synchronization and necessary conditions of Kalman's criterion. In addition, with the help of partial synchronization decomposition, a condition that the approximately synchronizable state does not depend on the sequence of boundary controls is also given. 相似文献
15.
We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions. 相似文献
16.
《Journal of Computational and Applied Mathematics》2005,174(2):315-327
We develop a new method of lower and upper solutions for a fourth-order nonlinear boundary value problem where the differential equation has dependence on all lower-order derivatives. Our boundary conditions are nonlinear. We will assume the functions that define the nonlinear boundary conditions are either monotone or nonmonotone. As a result we obtain existence principles which improve recent results in the literature. 相似文献
17.
We obtain necessary and sufficient conditions for the solvability of boundary value problems with one- and two-point boundary conditions. 相似文献
18.
《Applied Mathematics Letters》2006,19(8):735-740
We introduce new boundary conditions for large eddy simulation. These boundary conditions are based on an approximate deconvolution approach. They are computationally efficient and general, which makes them appropriate for the numerical simulation of turbulent flows with time-dependent boundary conditions. Numerical results are presented to demonstrate the new boundary conditions in a simplified linear setting. 相似文献
19.
S. Engleder 《Journal of Mathematical Analysis and Applications》2007,331(1):396-407
In this paper we describe some modified regularized boundary integral equations to solve the exterior boundary value problem for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. We formulate combined boundary integral equations which are uniquely solvable for all wave numbers even for Lipschitz boundaries Γ=∂Ω. This approach extends and unifies existing regularized combined boundary integral formulations. 相似文献
20.
Eun Heui Kim 《Journal of Differential Equations》2005,211(2):407-451
We present Hölder estimates and Hölder gradient estimates for a class of free boundary problems with tangential oblique derivative boundary conditions provided the oblique vector β does not vanish at any point on the boundary. We also establish the existence result for a general class of quasilinear degenerate problems of this type including nonlinear wave systems and the unsteady transonic small disturbance equation. 相似文献