共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal de Mathématiques Pures et Appliquées》1999,78(3):313-351
We consider Euler equations for an homogeneous incompressible non viscous fluid inside a smooth bounded domain of the plane. For an initial data of smooth vortex patch type, we obtain existence and uniqueness of a solution of the same type, locally in time if the initial patch is tangent to the boundary of the domain, and globally in time if the patch is far away from the boundary. We use pseudo-differential calculus to take care of the boundary condition. For the tangent limit case, we show that the velocity gradient of a vortex patch is Hölder continuous up to the boundary of the patch, using singular integrals. Our method provide also a result for several mutually tangent vortex patches in the plane. 相似文献
2.
Many important classes of decision models give rise to the problem of finding a global maximum of a convex function over a convex set. This problem is known also as concave minimization, concave programming or convex maximization. Such problems can have many local maxima, therefore finding the global maximum is a computationally difficult problem, since standard nonlinear programming procedures fail. In this article, we provide a very simple and practical approach to find the global solution of quadratic convex maximization problems over a polytope. A convex function achieves its global maximum at extreme points of the feasible domain. Since an inscribed ball does not contain any extreme points of the domain, we use the largest inscribed ball for an inner approximation while a minimal enclosing box is exploited for an outer approximation of the domain. The approach is based on the use of these approximations along with the standard local search algorithm and cutting plane techniques. 相似文献
3.
本文利用角动量作为Liapunov函数建立二维的圆形涡块及涡环在有限或无限区域上的(Liapunov)非线性稳定性. 相似文献
4.
Semi-hyperbolic patches are the regions in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves. This type of region appears frequently in the two-dimensional Riemann problem for the Euler equations and its simplified models and a few other situations. We construct a semi-hyperbolic patch of solution to the two-dimensional nonlinear wave system with Chaplygin gas equation of state by approaching the problem as a Goursat-type boundary value problem which has a sonic curve as the degenerate boundary. 相似文献
5.
The problem of characterizing extreme points of a family of polyhedra is considered. This family embraces a variety of linear
relaxations of feasible regions of discrete location problems. After characterizing the extreme points by means of a homogeneous
system of linear equations, we obtain, as particular cases, four problems which have already been treated from a polyhedral
point of view in the literature. Finally, we show that our characterization improves the one known for the Simple Plant Location
Problem and corrects the one established for the Two-Level Uncapacitated Facility Location Problem.
The first and third authors were supported by Fundación Séneca, project PB/11/FS/97 相似文献
6.
《数学物理学报(B辑英文版)》2017,(6)
This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all,we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain.Secondly,in order to determine that a bounded polyhedron is a discriminating domain,we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points(extreme points) and the existing ones need to verify all points in the bounded polyhedron. 相似文献
7.
Piermarco Cannarsa Genni Fragnelli Dario Rocchetti 《Journal of Evolution Equations》2008,8(4):583-616
We give null controllability results for some degenerate parabolic equations in non divergence form on a bounded interval.
In particular, the coefficient of the second order term degenerates at the extreme points of the domain. For this reason,
we obtain an observability inequality for the adjoint problem. Then we prove Carleman estimates for such a problem. Finally,
in a standard way, we deduce null controllability also for semilinear equations.
相似文献
8.
J. D. Mireles James 《Journal of Nonlinear Science》2013,23(4):585-615
We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex bubble. The vortex bubble, when present in the system, is the dominant feature in the phase space of the quadratic family, as it encloses all invariant dynamics. Our study focuses on visualizing qualitative features of the vortex bubble such as bifurcations in its geometry, the geometry of some three-dimensional homoclinic tangles associated with the bubble, and the “quasi-capture” of homoclinic orbits by neighboring fixed points. Throughout, we couple our results with previous qualitative numerical studies of the elliptic dynamics within the vortex bubble of the quadratic family. 相似文献
9.
We examine existence and stability of relative equilibria of the n-vortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the
weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be
used to characterize orbits and stability. Whenever a critical point of this function is nondegenerate, we prove that the
orbit can be continued via the Implicit Function Theorem, and its linear stability is determined by the eigenvalues of the
Hessian matrix of the potential. For N≥3 there are at least three distinct families of critical points associated to the limiting problem. Assuming nondegeneracy,
one of these families continues to a linearly stable class of relative equilibria with small and large circulation of the
same sign. This class becomes unstable as the small circulation passes through zero and changes sign. Another family of critical
points which is always nondegenerate continues to a configuration with small vortices arranged in an N-gon about the strong central vortex. This class of relative equilibria is linearly unstable regardless of the sign of the
small circulation when N≥4. Numerical results suggest that the third family of critical points of the limiting problem also continues to a linearly
unstable class of solutions of the full problem independent of the sign of the small circulation. Thus there is evidence that
linearly stable relative equilibria exist when the large and small circulation strengths are of the same sign, but that no
such solutions exist when they have opposite signs. The results of this paper are in contrast to those of the analogous celestial
mechanics problem, for which the N-gon is the only relative equilibrium for N sufficiently large, and is linearly stable if and only if N≥7. 相似文献
10.
In this paper we investigate the problem of existence of solutions for a super-critical fourth order Yamabe type equation and we exhibit a family of solutions concentrating at two points, provided the domain contains one hole and we give a multiplicity result if we are given multiple holes. 相似文献
11.
Chi-Kwong Li 《Linear and Multilinear Algebra》1985,18(2):117-125
In this note we give a unifying approach to the problem of characterizing the extreme points of those convex matrix sets which correspond to the domains of various types of capacitated network problems. It is shown that we can determine whether a matrix is an extreme point of the sets by examining the pattern of a certain graph associated with it. We also study the extreme points of the convex matrix sets which are related to network problems free from capacity constraints by linking them up with certain capacitated network problem. 相似文献
12.
In this article the mean-field vortex model arising from the II-type superconductivity is investigated. The vortex model is reduced to a nonlinear hyperbolic–elliptic system of PDEs in a bounded domain. Motivated by experiments, we consider physical boundary conditions, which describe a flux of superconducting vortices through the boundary of the domain. We prove the global solvability for the system. To show the solvability result we take a vanishing “viscosity” limit in an approximated parabolic–elliptic system. Since the approximated solutions do not have a compactness property, we justify this limit transition, using a kinetic formulation of our problem. The main trick is that instead of the nonlinear system, we have to investigate a linear transport equation. 相似文献
13.
利用生存性理论, 研究线性微分博弈系统的一个有界识别域问题. 采用生存性理论来研究线性微分博弈系统的有界多面体\,(有限点集的凸包)\,的识别域问题, 给定的方法只需要检验该多面体在极点处是否满足生存性条件. 进而, 利用生存性与识别域的关系, 即可判断此多面体是否是系统的识别域, 简便易行. 相似文献
14.
15.
MICHAEL J. WARD 《Natural Resource Modeling》2000,13(2):271-302
ABSTRACT. Diffusion problems under singular perturbations of the domain or the boundary conditions are analyzed. The first problem that we consider is the diffusion of a material from a domain that is nearly impermeable, having only several small patches on the boundary where the material can slowly leak out. The second problem that is studied is the diffusion of a material that originates from some localized regions in a two or three‐dimensional domain. Steady‐state solutions and the long‐time behavior of solutions are analyzed in detail. Finally, the analysis is extended to determine the change in bifurcation values associated with nonlinear diffusion equations under singular perturbations of the domain. The results are then applied to a model in resource management. 相似文献
16.
Recently Andersen et al. [1], Borozan and Cornuéjols [6] and Cornuéjols and Margot [9] have characterized the extreme valid inequalities of a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex sets. In order to use these inequalities to obtain cuts from two rows of a general simplex tableau, one approach is to extend the system to include all possible non-negative integer variables (giving the two row mixed-integer infinite-group problem), and to develop lifting functions giving the coefficients of the integer variables in the corresponding inequalities. In this paper, we study the characteristics of these lifting functions. We show that there exists a unique lifting function that yields extreme inequalities when starting from a maximal lattice-free triangle with multiple integer points in the relative interior of one of its sides, or a maximal lattice-free triangle with integral vertices and one integer point in the relative interior of each side. In the other cases (maximal lattice-free triangles with one integer point in the relative interior of each side and non-integral vertices, and maximal lattice-free quadrilaterals), non-unique lifting functions may yield distinct extreme inequalities. For the latter family of triangles, we present sufficient conditions to yield an extreme inequality for the two row mixed-integer infinite-group problem. 相似文献
17.
In this paper an algorithm is developed to generate all nondominated extreme points and edges of the set of objective values of a multiple objective linear program. The approach uses simplex tableaux but avoids generating unnecessary extreme points or bases of extreme points. The procedure is based on, and improves, an algorithm Dauer and Liu developed for this problem. Essential to this approach is the work of Gal and Kruse on the neighborhood problem of determining all extreme points of a convex polytope that are adjacent to a given (degenerate) extreme point of the set. The algorithm will incorporate Gal's degeneracy graph approach to the neighborhood problem with Dauer's objective space analysis of multiple objective linear programs. 相似文献
18.
19.
《European Journal of Operational Research》2005,162(2):484-496
In this paper we employ regression analysis to construct relationships for predicting the number of efficient extreme points in MOLPs (multiple objective linear programs) with up to 120,000 efficient extreme points, and the CPU time to compute them. Principal among the factors affecting the number of efficient extreme points and CPU time are the number of objectives, criterion cone size, number of constraints, number of variables, and the nonzero density of the constraint matrix. The regression equations show the degree to which interactions are present among the factors and provide a more formal basis for understanding how the complexity of the efficient set, an indicator of the difficulty involved in solving a multiple criteria problem, increases with problem size. 相似文献
20.
Katta G. Murty 《Optimization Letters》2009,3(2):211-237
We consider the problem of developing an efficient algorithm for enumerating the extreme points of a convex polytope specified
by linear constraints. Murty and Chung (Math Program 70:27–45, 1995) introduced the concept of a segment of a polytope, and used it to develop some steps for carrying out the enumeration efficiently until the convex hull of the
set of known extreme points becomes a segment. That effort stops with a segment, other steps outlined in Murty and Chung (Math
Program 70:27–45, 1995) for carrying out the enumeration after reaching a segment, or for checking whether the segment is
equal to the original polytope, do not constitute an efficient algorithm. Here we describe the central problem in carrying
out the enumeration efficiently after reaching a segment. We then discuss two procedures for enumerating extreme points, the
mukkadvayam checking procedure, and the nearest point procedure. We divide polytopes into two classes: Class 1 polytopes have
at least one extreme point satisfying the property that there is a hyperplane H through that extreme point such that every facet of the polytope incident at that extreme point has relative interior point
intersections with both sides of H; Class 2 polytopes have the property that every hyperplane through any extreme point has at least one facet incident at that
extreme point completely contained on one of its sides. We then prove that the procedures developed solve the problem efficiently
when the polytope belongs to Class 2. 相似文献