共查询到20条相似文献,搜索用时 15 毫秒
1.
On the condition that the interval of the problem shrinks to a point, we investigated the separated boundary conditions S α,β of left-definite Sturm-Liouville problem, and answered the following question: Is there a c 0 ∈ J such that S α,β is always left-definite or semi-left-definite for the Sturm-Liouville equation for each c ∈ (a, c 0 )? 相似文献
2.
A. A. Solov'ev 《Mathematical Notes》1996,59(6):637-645
The boundary equations of the logarithmic potential theory corresponding to the interior Dirichlet problem and the exterior
Neumann problem for a plane domain with a cusp on the boundary are studied. Solvability theorems are proved for these integral
equations in the spacesL
p.
Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 881–892, June, 1996. 相似文献
3.
E. Shmoylova S. Potapenko L. Rothenburg 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,86(1):506-522
In this paper we formulate interior Dirichlet and Neumann boundary value problems of plane Cosserat elasticity in Sobolev
spaces, show that these problems are well-posed and find the corresponding weak solutions in the form of integral potentials. 相似文献
4.
E. Shmoylova S. Potapenko L. Rothenburg 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):506-522
In this paper we formulate interior Dirichlet and Neumann boundary value problems of plane Cosserat elasticity in Sobolev
spaces, show that these problems are well-posed and find the corresponding weak solutions in the form of integral potentials.
Received: April 7, 2005 相似文献
5.
Solving real-world linear ordering problems using a primal-dual interior point cutting plane method 总被引:2,自引:0,他引:2
Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplex-based cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some real-world problems; the algorithm appears to be competitive with a simplex-based cutting plane algorithm.Research partially supported by ONR Grant number N00014-90-J-1714. 相似文献
6.
Emma Skopin 《PAMM》2012,12(1):585-586
The scalar Oseen equation represents a linearized form of the Navier Stokes equations. We present an explicit potential theory for this equation and solve the exterior Dirichlet and interior Neumann boundary value problems via a boundary integral equations method in spaces of continuous functions on a C2-boundary, extending the classical approach for the isotropic selfadjoint Laplace operator to the anisotropic non-selfadjoint scalar Oseen operator. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987. 相似文献
8.
The boundary value problem for the Laplace equation is studied on a domain with smooth compact boundary and with smooth internal cracks. The Neumann or the Robin condition is given on the boundary of the domain. The jump of the function and the jump of its normal derivative is prescribed on the cracks. The solution is looked for in the form of the sum of a single layer potential and a double layer potential. The solvability of the corresponding integral equation is determined and the explicit solution of this equation is given in the form of the Neumann series. Estimates for the absolute value of the solution of the boundary value problem and for the absolute value of the gradient of the solution are presented. 相似文献
9.
N. Odishelidze F. Criado-Aldeanueva F. Criado J. M. Sanchez 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(1):193-200
The paper addresses a problem of plane elasticity theory for a doubly connected body whose external boundary is a regular hexagon boundary, and the internal boundary is the required full-strength hole including the origin of coordinates. Hexagon’s two vertices are laid at the axis Oy, and the middle points of its two opposite sides are laid at the axis Ox. This full-strength hole is cycle symmetric. It is assumed that to every link of the broken line of the outer boundary of the given body are applied absolutely smooth rigid stamps with rectilinear bases, which are under action of the force P that applies to their middle points. There is no friction between the surface of given elastic body and stamps. The unknown full-strength contour is free from outer actions. Using the methods of complex analysis, the analytical image of Kolosov–Muskhelishvili’s complex potentials (characterizing an elastic equilibrium of the body) and unknown parts of its boundary are determined under the condition that the tangential normal moment arising at it takes a constant value. Such holes are called full-strength holes. Numerical analysis are also performed and the corresponding graphs are constructed. 相似文献
10.
For a smooth domain with compact boundary we investigate the problem with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that is sufficiently small we show the existence of at least positive solutions with single maximum points that lie on . We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space .
Received May 25, 1997 / Accepted October 3, 1997 相似文献
11.
12.
Maryse Bourlard Serge Nicaise Luc Paquet 《Mathematical Methods in the Applied Sciences》1990,12(3):251-265
The Neumann problem for Laplace's equation in a polygonal domain is associated with the exterior Dirichlet problem obtained by requiring the continuity of the potential through the boundary. Then the solution is the simple layer potential of the charge q on the boundary. q is the solution of a Fredholm integral equation of the second kind that we solve by the Galerkin method. The charge q has a singular part due to the corners, so the optimal order of convergence is not reached with a uniform mesh. We restore this optimal order by grading the mesh adequately near the corners. The interior Dirichlet problem is solved analogously, by expressing the solution as a double layer potential. 相似文献
13.
In this paper we are concerned with the following Neumann problem
14.
We consider the following singularly perturbed Neumann problem: where Δ = Σ ?2/?x is the Laplace operator, ? > 0 is a constant, Ω is a bounded, smooth domain in ?N with its unit outward normal ν, and f is superlinear and subcritical. A typical f is f(u) = up where 1 < p < +∞ when N = 2 and 1 < p < (N + 2)/(N ? 2) when N ≥ 3. We show that there exists an ?0 > 0 such that for 0 < ? < ?0 and for each integer K bounded by where αN, Ω, f is a constant depending on N, Ω, and f only, there exists a solution with K interior peaks. (An explicit formula for αN, Ω, f is also given.) As a consequence, we obtain that for ? sufficiently small, there exists at least [αN, Ωf/?N (|ln ?|)N] number of solutions. Moreover, for each m ∈ (0, N) there exist solutions with energies in the order of ?N?m. © 2006 Wiley Periodicals, Inc. 相似文献
15.
Summary
Existence theorems for nonlinear Neumann problems with inhomogeneous boundary conditions are established. It is then investigated under which conditions the solutions are uniformly bounded. Uniqueness results for positive solutions are given and the asymptotic behavior of the solutions of the corresponding parabolic equation is discussed. The main tools are fixed point theorems and the method of upper and lower solutions. 相似文献
16.
We study the structure of positive solutions to the equation ?mΔmu-um-1+f(u)=0 with homogeneous Neumann boundary condition. First, we show the existence of a mountain-pass solution and find that as ?→0+ the mountain-pass solution develops into a spike-layer solution. Second, we prove that there is an uniform upper bound independent of ? for any positive solution to our problem. We also present a Harnack-type inequality for the positive solutions. Finally, we show that if 1<m?2 holds and ? is sufficiently large, any positive solution must be a constant. 相似文献
17.
I.B. Badriyev O.A. Zadvornov L.N. Ismagilov E.V. Skvortsov 《Journal of Applied Mathematics and Mechanics》2009,73(4):434-442
The steady seepage of an incompressible fluid in a uniform porous medium, occupying an arbitrary bounded two-dimensional region, when there is a point source present is considered. Part of the boundary of the region is free, while the remaining part is impermeable for the fluid. It is assumed that the function defining the seepage law is multivalued and has a linear increase at infinity. A generalized formulation of the problem is proposed in the form of a variational inequality of the second kind. An approximate solution of the problem is obtained by an iterative splitting method, which enables approximate values of both the solution itself (the pressure) and its gradient to be found. Analytic expressions describing the boundaries of the region where the modulus of the pressure gradient takes a constant value are obtained for model problems of a line of bore holes. Numerical experiments are carried out for model problems, which confirm the effectiveness of the proposed method. Good agreement is observed between the results of calculations obtained analytically and by approximate methods. 相似文献
18.
A. N. Agalakov S. B. Raevskii A. A. Titarenko 《Computational Mathematics and Mathematical Physics》2011,51(10):1746-1755
An approach based on a modified Galerkin method is proposed for solving interior diffraction problems. The solution procedure
is demonstrated by computing the junction of two planar waveguides through a waveguide segment filled with an arbitrary dielectric
material. 相似文献
19.
P. A. Krutitskii 《Differential Equations》2013,49(9):1062-1074
We consider a boundary value problem for harmonic functions outside cuts on the plane. The jump of the normal derivative and a linear combination of the normal derivative on one side with the jump of the unknown function are given on each cut. The problem is considered with three conditions at infinity, which lead to distinct results on the existence and number of solutions. We obtain an integral representation of the solution in the form of potentials whose density satisfies a uniquely solvable Fredholm integral equation of the second kind. 相似文献
20.
We prove that the solution of the Neumann problem for the Helmholtz equation in a plane angle Ω with boundary conditions from the space H−1/2(Γ), where Γ is the boundary of Ω, which is provided by the well‐known Sommerfeld integral, belongs to the Sobolev space H1(Ω) and depends continuously on the boundary values. To this end, we use another representation of the solution given by the inverse two‐dimensional Fourier transform of an analytic function depending on the Cauchy data of the solution. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献