共查询到20条相似文献,搜索用时 31 毫秒
1.
Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
2.
In this paper we study which solutions to an embedding problem can be constructed using a versal deformation of a group representation
over an algebraically closed field of positive characteristic. This question reduces (at least stably) to finding which representations
of finite groups have faithful versal deformations. We determine exactly when a versal deformation of a representation of
a finite group is faithful in case the representation belongs to a cyclic block and its endomorphisms are given by scalar
multiplications.
Received: January 30, 2001 相似文献
3.
4.
Henry C. Wente 《Calculus of Variations and Partial Differential Equations》2002,14(2):193-211
We consider large solutions of annular type to the volume constrained Douglas problem. They are conformally immersed H-surfaces. By rescaling we set the volume functional at one while the boundary curves shrink to the origin. We show that the
solutions become spherical in a precise manner. Spherical bubbling may fail if the conformality condition is dropped. We also
discuss the rotationally symmetric annular solutions to the H-surface equation and consider some illustrative examples.
Received: 2 May 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001 相似文献
5.
We introduce a suitable concept of approximate social Nash equilibrium and we determine sufficient conditions of minimal character which guarantee, for a parametric social Nash equilibrium problem, the lower semicontinuity of the set-valued function defined by these approximate solutions.
Received: December 2001 相似文献
6.
V. Mityushev 《Applied Mathematics and Optimization》2001,44(1):17-31
We solve an R -linear problem for a multiple-connected circular domain in a class of doubly periodic functions in analytic
form by a method of functional equations. This problem models transport properties of two-dimensional composite materials
made from a collection of disks embedded in an otherwise uniform host.
Accepted 25 January 2001. Online publication 26 May 2001. 相似文献
7.
Thomas H. Otway 《Annali di Matematica Pura ed Applicata》2002,181(4):437-452
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which
reduces to the equations for harmonic 1-forms on the projective disc is studied in detail. A boundary-value problem for this
example is formulated and shown to possess weak solutions.
Received: May 16, 2001; in final form: September 24, 2001?Published online: October 30, 2002 相似文献
8.
Motivated by the construction of selfgravitating strings (cf. Yang, 2001, 1994 [22], [23]), we analyze a Liouville-type equation on the plane, derived in Yang (1994) [23]. We establish sharp existence and uniqueness properties for the corresponding radial solutions. We investigate also when the problem allows for non-radial solutions. 相似文献
9.
This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence
of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation
as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions
of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints,
we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last
one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive
Pontryagin's principles for problems with pointwise state constraints.
Accepted 12 July 2001. Online publication 21 December 2001. 相似文献
10.
We study a discrete optimization problem introduced by Babai, Frankl, Kutin, and Štefankovi? (2001), which provides bounds on degrees of polynomials with p-adically controlled behavior. Such polynomials are of particular interest because they furnish bounds on the size of set systems satisfying Frankl-Wilson-type conditions modulo prime powers, with lower degree polynomials providing better bounds. We elucidate the asymptotic structure of solutions to the optimization problem, and we also provide an improved method for finding solutions in certain circumstances. 相似文献
11.
Andrea Malchiodi 《Calculus of Variations and Partial Differential Equations》2002,14(4):429-445
We prove the existence of positive solutions for the equation on , where is the Laplace-Beltrami operator on is the critical Sobolev exponent, and is a small parameter. The problem can be reduced to a finite dimensional study which is performed via Morse theory.
Received: 29 September 1999 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献
12.
Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model 总被引:4,自引:0,他引:4
Summary. A positivity-preserving numerical scheme for a strongly coupled cross-diffusion model for two competing species is presented,
based on a semi-discretization in time. The variables are the population densities of the species. Existence of strictly positive
weak solutions to the semidiscrete problem is proved. Moreover, it is shown that the semidiscrete solutions converge to a
non-negative solution of the continuous system in one space dimension. The proofs are based on a symmetrization of the problem
via an exponential transformation of variables and the use of an entropy functional.
Received September 10, 2001 / Revised version received February 25, 2002 / Published online June 17, 2002 相似文献
13.
Summary. We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave
regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an infinite-dimensional
family. We characterize these solutions through spatial dynamics, by reducing a linearly ill-posed mixed-type initial-value
problem to a center manifold of infinite dimension and codimension. A unique global solution exists for arbitrary small initial
data for the two-component bottom velocity, specified along a single line in the direction of translation (or orthogonal to
it). A dispersive, nonlocal, nonlinear wave equation governs the spatial evolution of bottom velocity.
Received July 20, 2001; accepted November 5, 2001 相似文献
14.
Summary. We investigate global equilibria of twisted, isotropic elastic rings. The high degree of symmetry in the problem leads to
nonisolated solutions. We prove that all solutions are flip-symmetric, and from this we can globally isolate all solution branches. We derive possible other choices
for boundary conditions systematically and show that other conditions necessarily lead to spurious solutions. We show global computations performed by the Parallel Simplex Algorithm.
Received March 26, 2000; accepted September 19, 2000 Online publication February 26, 2001 相似文献
15.
We obtain selfgravitating multi-string configurations for the Einstein-Weinberg-Salam model, in terms of solutions for a nonlinear elliptic system of Liouville type whose solvability was posed as an open problem in Yang (Solitons in Field Theory and Nonlinear Analysis, Springer, New York, 2001). 相似文献
16.
Stéphane Alarie Charles Audet Brigitte Jaumard Gilles Savard 《Mathematical Programming》2001,90(2):373-398
We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent
symmetric linear maxmin reformulations, leading to two sets of concavity cuts. We first examine the depth of these cuts by
considering the assumptions on the boundedness of the feasible regions of both maxmin and bilinear formulations. We next propose
a branch and bound algorithm which make use of concavity cuts. We also present a procedure that eliminates degenerate solutions.
Extensive computational experiences are reported. Sparse problems with up to 500 variables in each disjoint sets and 100 constraints,
and dense problems with up to 60 variables again in each sets and 60 constraints are solved in reasonable computing times.
Received: October 1999 / Accepted: January 2001?Published online March 22, 2001 相似文献
17.
We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for
which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove
uniqueness and a comparison principle in for these solutions. To prove the existence we use the nonlinear semigroup theory.
Received: 26 October 2000 / Revised version: 1 May 2001 / Published online: 24 September 2001 相似文献
18.
Hardeep S. Gill 《Stochastic Processes and their Applications》2009,119(12):3981-4003
We construct a class of interactive measure-valued diffusions driven by a historical super-Brownian motion and an independent white noise by solving a certain stochastic equation. In doing so, we show that the approach of Perkins (2002) [3] can be used to study the problem examined by Dawson et al. (2001) [1]. This unifies and extends both Dawson et al. (2001) [1] and Perkins (2002) [3] and establishes a new class of measure-valued diffusions. The existence and pathwise uniqueness of the solutions are proved, and the solutions are shown to satisfy the natural martingale problem. 相似文献
19.
J. U. Kim 《Applied Mathematics and Optimization》2001,44(1):33-48
In this paper we discuss an initial—boundary value problem for an elastic plate driven by a space-time white noise. The existence
and uniqueness of a weak solution is established. We use a specialized PDE method based upon the results for the deterministic
equation.
Accepted 2 February 2001. Online publication 4 May 2001. 相似文献
20.
Summary. In this paper we consider a frictionless contact problem between an elastic–viscoplastic body and an obstacle. The process
is assumed to be quasistatic and the contact is modeled with normal compliance. We present a variational formulation of the
problem and prove the existence and uniqueness of the weak solution, using strongly monotone operators arguments and Banach's
fixed point theorem. We also study the numerical approach to the problem using spatially semi-discrete and fully discrete
finite elements schemes with implicit and explicit discretization in time. We show the existence of the unique solution for
each of the schemes and derive error estimates on the approximate solutions. Finally, we present some numerical results involving
examples in one, two and three dimensions.
Received May 20, 2000 / Revised version received January 8, 2001 / Published online June 7, 2001 相似文献