共查询到20条相似文献,搜索用时 15 毫秒
1.
Ibrahim K. Djire 《复变函数与椭圆型方程》2016,61(8):1133-1144
We present some basic properties of the so-called boundary relative extremal function and discuss boundary pluripolar sets and boundary pluripolar hulls. We show that for B-regular domains the boundary pluripolar hull is always trivial on the boundary of the domain and present a “boundary version” of Zeriahi’s theorem on the completeness of pluripolar sets. 相似文献
2.
John Andersson 《Journal of Differential Equations》2007,232(1):285-302
We investigate the regularity of a free boundary near contact points with a fixed boundary, with C1,1 boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C1 up to the fixed boundary. We will also construct some examples of irregular free boundaries. 相似文献
3.
Greg Friedman 《Israel Journal of Mathematics》2008,163(1):139-188
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots D
n−2 ↪ D
n
. Any two disk knots are cobordant if the cobordisms are not required to fix the boundary sphere knots, and any two even-dimensional
disk knots with isotopic boundary knots are cobordant rel boundary. However, the cobordism rel boundary theory of odd-dimensional
disk knots is more subtle. Generalizing results of J. Levine on the cobordism of sphere knots, we define disk knot Seifert
matrices and show that two higher-dimensional disk knots with isotopic boundaries are cobordant rel boundary if and only if
their disk knot Seifert matrices are algebraically cobordant. We also ask which algebraic cobordism classes can be realized
given a fixed boundary knot and provide a complete classification when the boundary knot has no 2-torsion in its middle-dimensional
Alexander module.
In the course of this classification, we establish a close connection between the Blanchfield pairing of a disk knot and the
Farber-Levine torsion pairing of its boundary knot (in fact, for disk knots satisfying certain connectivity assumptions, the
disk knot Blanchfield pairing will determine the boundary Farber-Levine pairing). In addition, we study the dependence of
disk knot Seifert matrices on choices of Seifert surface, demonstrating that all such Seifert matrices are rationally S-equivalent, but not necessarily integrally S-equivalent. 相似文献
4.
Desheng Yang 《随机分析与应用》2013,31(3):613-639
Abstract Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition involves the time derivative as well as spatial derivatives for the system state variables on the boundary. Although stochastic static (Neumann or Dirichet type) boundary conditions have been applied for stochastic partial differential equations, not much is known about the dynamical impact of stochastic dynamic boundary conditions. The purpose of this article is to study possible impacts of stochastic dynamic boundary conditions on the long term dynamics of the Cahn-Hilliard equation arising in the materials science. We show that the dimension estimation of the random attractor increases as the coefficient for the dynamic term in the stochastic dynamic boundary condition decreases. However, the dimension of the random attractor is not affected by the corresponding stochastic static boundary condition. 相似文献
5.
Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data 下载免费PDF全文
Helmut Harbrecht Giannoula Mitrou 《Mathematical Methods in the Applied Sciences》2015,38(13):2850-2863
We apply the trial method for the solution of Bernoulli's free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation, and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach's fixed‐point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings.Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
H. P. Lopushans’ka 《Ukrainian Mathematical Journal》2009,61(4):566-591
In weighted C-spaces, we establish the solvability of a boundary-value problem for a semilinear elliptic equation of order 2m in a bounded domain with generalized functions given on its boundary, strong power singularities at some points of the boundary,
and finite orders of singularities on the entire boundary. The behavior of the solution near the boundary of the domain is
analyzed. 相似文献
7.
A.T. Peplow S.N. Chandler-Wilde 《Journal of Mathematical Analysis and Applications》2008,345(1):305-321
The paper considers the solution of the boundary value problem (BVP) consisting of the Helmholtz equation in the region D with a rigid boundary condition on ∂D and its reformulation as a boundary integral equation (BIE), over an infinite cylindrical surface of arbitrary smooth cross-section. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution of the integral equation and the corresponding boundary value problem. 相似文献
8.
Construction of Solutions and L^1-error Estimates of Viscous Methods for Scalar Conservation Laws with Boundary 总被引:4,自引:0,他引:4
Hong Xia LIU Tao PAN 《数学学报(英文版)》2007,23(3):393-410
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O(ε^1/2) in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O(ε| In ε|). 相似文献
9.
Continuing our work on the boundary value problem for super-Liouville equation, we study the qualitative behavior of boundary blow-ups. The boundary condition is derived from the chirality conditions in the physics literature, and is geometrically natural. In technical terms, we derive a new Pohozaev type identity and provide a new alternative, which also works at the boundary, to the classical method of Brézis–Merle. 相似文献
10.
YAKUBOV Yakov 《中国科学 数学(英文版)》2013,56(1):105-122
This paper is a continuation of the author’s paper in 2009,where the abstract theory of fold completeness in Banach spaces has been presented.Using obtained there abstract results,we consider now very general boundary value problems for ODEs and PDEs which polynomially depend on the spectral parameter in both the equation and the boundary conditions.Moreover,equations and boundary conditions may contain abstract operators as well.So,we deal,generally,with integro-differential equations,functional-differential equations,nonlocal boundary conditions,multipoint boundary conditions,integro-differential boundary conditions.We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework,in contrast to previously known results in the Hilbert L 2-framework.Some concrete mechanical problems are also presented. 相似文献
11.
In this paper we continue the study in Lewis and Nyström (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph. 相似文献
12.
A homogeneous elastic body with stress-free boundary is considered. The boundary of the body, which consists of a smooth cylindrical
surface and a half-plane, has a continuous tangent plane, but the curvature of the normal section of the boundary has a discontinuity
of the first kind at each point of the junction line. The behavior of two kinds of “whispering gallery” transversal surface
waves at transition through the junction line is studied. For waves of the first kind (corresponding to Dirichlet boundary
conditions), the displacement vector is normal to the boundary, whereas for waves of the second kind (corresponding to Neumann
boundary conditions) the displacement vector is tangent to the boundary and normal to the ray, similarly to the case of Love
waves. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 86–102.
Translated by N. Ya. Kirpichnikova. 相似文献
13.
Verena Bögelein Frank Duzaar Giuseppe Mingione 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
This is the second part of a work aimed at establishing that for solutions to Cauchy–Dirichlet problems involving general non-linear systems of parabolic type, almost every parabolic boundary point is a Hölder continuity point for the spatial gradient of solutions. Here we establish higher fractional differentiability of solutions up to the boundary. Based on the necessary and sufficient condition for regular boundary points from the first part of Bögelein et al. (in this issue)[7] we achieve dimension estimates for the boundary singular set and eventually the almost everywhere regularity of solutions at the boundary. 相似文献
14.
Temur Jangveladze Zurab Kiguradze Beny Neta 《Journal of Mathematical Analysis and Applications》2009,351(1):382-6892
Asymptotic behavior of solutions as t→∞ to the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. Initial-boundary value problems with two kinds of boundary data are considered. The first with homogeneous conditions on whole boundary and the second with non-homogeneous boundary data on one side of lateral boundary. The rates of convergence are given too. 相似文献
15.
Computational homogenization of materials with small deformation to determine configurational forces
In this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE2 approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.
17.
Christopher D. Sogge 《偏微分方程通讯》2017,42(8):1249-1289
We prove that the Cauchy data of Dirichlet or Neumann Δ- eigenfunctions of Riemannian manifolds with concave (diffractive) boundary can only achieve maximal sup norm bounds if there exists a self-focal point on the boundary, i.e., a point at which a positive measure of geodesics leaving the point return to the point. In the case of real analytic Riemannian manifolds with real analytic boundary, maximal sup norm bounds on boundary traces of eigenfunctions can only be achieved if there exists a point on the boundary at which all geodesics loop back. As an application, the Dirichlet or Neumann eigenfunctions of Riemannian manifolds with concave boundary and non-positive curvature never have eigenfunctions whose boundary traces achieve maximal sup norm bounds. The key new ingredient is the Melrose–Taylor diffractive parametrix and Melrose’s analysis of the Weyl law. 相似文献
18.
Kazuaki Taira 《Journal of Evolution Equations》2013,13(2):481-507
This paper is devoted to a semigroup approach to an initial-boundary value problem of linear elastodynamics in the case where the boundary condition is a regularization of the genuine mixed displacement-traction boundary condition. More precisely, it is a smooth linear combination of displacement and traction boundary conditions, but is not equal to the pure traction boundary condition. Some previous results with mixed displacement-traction boundary condition are due to Inoue and Ito. The crucial point in our semigroup approach is to generalize the classical variational approach to the degenerate case, by using the theory of fractional powers of analytic semigroups. 相似文献
19.
This paper applies the technique of the h–p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proved when a geometric mesh refinement towards the vertices is used. 相似文献
20.
A class of singularly perturbed boundary value problem with singularities is considered. Introducing the stretched variables, the boundary layer corrective terms near x = 0 and x = 1 are constructed. Under suitable conditions, by using the theory of differential inequalities the existence and asymptotic behavior of solution for boundary value problem are proved, uniformly valid asymptotic expansion of solution with boundary layers are obtained, 相似文献