共查询到20条相似文献,搜索用时 78 毫秒
1.
P. Karamian‐Surville J. Sanchez‐Hubert E. Sanchez Palencia 《Mathematical Methods in the Applied Sciences》2003,26(17):1451-1485
We consider problems of statics of thin elastic shells with hyperbolic middle surface subjected to boundary conditions ensuring the geometric rigidity of the surface. The asymptotic behaviour of the solutions when the relative thickness tends to zero is then given by the membrane approximation. It is a hyperbolic problem propagating singularities along the characteristics. We address here the reflection phenomena when the propagated singularities arrive to a boundary. As the boundary conditions are not the classical ones for a hyperbolic system, there are various cases of reflection. Roughly speaking, singularities provoked elsewhere are not reflected at all at a free boundary, whereas at a fixed (or clamped) boundary the reflected singularity is less singular than the incident one. Reflection of singularities provoked along a non‐characteristic curve C are also considered. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
We deal with singular perturbations of nonlinear problems depending on a small parameter ε > 0. First we consider the abstract theory of singular perturbations of variational inequalities involving some nonlinear
operators, defined in Banach spaces, and describe the asymptotic behavior of these solutions as ε → 0. Then these abstract results are applied to some boundary value problems. Bibliography: 15 titles. 相似文献
3.
Dingshijin LiuZuhan 《高校应用数学学报(英文版)》1997,12(1):77-88
In this paper, the asymptotic behavior as ε→O of the minimizers u,of the Ginzburg Lan-dau functional with variable coefficient is discussed. The singularities are found to be located at thepoints which globally minimize the coefficient. The zeros of u, are accumulated near the singulari-ties as is small enough. This verifies the pinning mechanism. 相似文献
4.
G. A. Chechkin 《Journal of Mathematical Sciences》2006,139(1):6351-6362
A problem for the Laplace operator is considered in a three-dimensional unbounded domain with singular density. The density,
depending on a small positive parameter ε, is equal to 1 outside small inclusions, and is equal to (δε)−m in these inclusions. These domains, concentrated masses of diameter εδ, are located along the plane part of the boundary
at the distance of order O(δ), where δ = δ(ε). The Dirichlet condition is imposed on the boundary parts tangent to the concentrated
masses. We construct the limit (averaged) operator and study the asymptotic behavior of solutions to the original problem
with m < 1.
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Translated from Problemy Matematicheskogo Analiza, No. 33, 2006, pp. 103–111. 相似文献
5.
B. Amaziane M. Goncharenko L. Pankratov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):592-611
The aim of this paper is to study the asymptotic behavior of the solution of a convection–diffusion equation in perforated
domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles.
Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find
the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection–diffusion
equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate
the methodology. 相似文献
6.
B. Amaziane M. Goncharenko L. Pankratov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,123(5):592-611
The aim of this paper is to study the asymptotic behavior of the solution of a convection–diffusion equation in perforated
domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles.
Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find
the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection–diffusion
equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate
the methodology. 相似文献
7.
Vladimir Semenovich Korolyuk 《Journal of Mathematical Sciences》2011,179(2):273-289
Three main schemes of limit theorems for random evolutions are discussed: averaging, diffusion approximation, and the asymptotics
of large deviations. Markov stochastic evolutions with locally independent increments on increasing time intervals T
ε
= t/ε → ∞, ε → 0, are considered. The asymptotic behavior of random evolutions is investigated with the use of solutions of the singular perturbation
problems for reducibly invertible operators. 相似文献
8.
We consider the M/G/1 queue with an arrival rate λ that depends weakly upon time, as λ = λ(εt) where ε is a small parameter. In the asymptotic limit ε → 0, we construct approximations to the probability p
n(t)that η customers are present at time t. We show that the asymptotics are different for several ranges of the (slow) time scale Τ= εt. We employ singular perturbation techniques and relate the various time scales by asymptotic matching.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, , in the neighbourhood of isolated singularities in the standard Euclidean ball. Although asymptotic radial symmetry for such
solutions was proved some time ago, [2], we present a much simpler and more geometric derivation of this fact. We also discuss
a refinement, showing that any such solution is asymptotic to one of the deformed radial singular solutions. Finally we give
some applications of these refined asymptotics, first to computing the global Pohožaev invariants of solutions on the sphere
with isolated singularities, and then to the regularity of the moduli space of all such solutions.
Oblatum 26-II-1997 & 6-II-1998 / Published online: 12 November 1998 相似文献
10.
S. A. Nazarov 《Journal of Mathematical Sciences》2010,167(5):713-725
An asymptotic model is found for the Neumann problem for the second-order differential equation with piecewise constant coefficients
in a composite domain Ω∪ω, which are small, of order ε, in the subdomain ω. Namely, a domain Ω(ε) with a singular perturbed
boundary is constructed, the solution for which provides a two-term asymptotic, that is, of increased accuracy O(ε2| log ε|3/2), approximation to the restriction to Ω of the solution of the original problem. As opposed to other singularly perturbed
problems, in the case of contrasting stiffness, the modeling requires the construction of a contour ∂Ω(ε) with ledges, i.e.,
with boundary fragments of curvature O(ε−1). Bibliography: 33 titles. 相似文献
11.
We present the asymptotic analysis of a quasilinear hyperbolic–hyperbolic singular perturbation problem in one dimension. The leading part of the analysis concerns the construction of some shock layers associated with discontinuities of a hyperbolic problem. This study is a generalization of the case of viscous perturbation for a hyperbolic problem. 相似文献
12.
In this paper we focus on approximate minimal points of a set in Hausdorff locally convex spaces. Our aim is to develop a
general framework from which it is possible to deduce important properties of these points by applying simple results. For
this purpose we introduce a new concept of ε-efficient point based on set-valued mappings and we obtain existence results and properties on the behavior of these approximate
efficient points when ε is fixed and by considering that ε tends to zero. Finally, the obtained results are applied to vector optimization problems with set-valued mappings. 相似文献
13.
Yu. A. Konyaev 《Mathematical Notes》1999,65(6):701-704
Singularly perturbed initial boundary value problems are studied for some classes of linear systems of ordinary differential
equations on the semiaxis with an unbounded spectrum of the limit operator. We give a new version of the proof of the existence
of a unique and bounded (as ε→+0) solution for which with the help of the splitting method we construct a uniform asymptotic
expansion on the entire semiaxis and describe all singularities (reflecting the structure of the corresponding boundary layers)
in closed analytic form, including the critical case in which the points of the spectrum of the limit operator can touch the
imaginary axis; this supplements previous results.
Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 831–835, June, 1999. 相似文献
14.
We consider a parabolic Signorini boundary value problem in a thick plane junction Ω
ε
which is the union of a domain Ω0 and a large number of ε−periodically situated thin rods. The Signorini conditions are given on the vertical sides of the thin rods. The asymptotic
analysis of this problem is done as ε → 0, i.e., when the number of the thin rods infinitely increases and their thickness tends to zero. With the help of the
integral identity method we prove a convergence theorem and show that the Signorini conditions are transformed (as ε → 0) in differential inequalities in the region that is filled up by the thin rods in the limit passage. Bibliography: 31
titles. Illustrations: 1 figure. 相似文献
15.
Alain Campbell 《Mathematical Methods in the Applied Sciences》2005,28(5):505-524
The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determine this spectrum and the weakness directions in the shell. We particularly study the case of homogeneous and isotropic shells with some examples. In the second part, we consider an elementary model problem to study the propagation of singularities and their reflections at the boundary of the domain. In the last, we study the problem of propagation for an isotropic cylindrical shell and we show that the equation of propagation does not depend on the Poisson coefficient. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
16.
Jean-Marc Schlenker 《Discrete and Computational Geometry》2008,40(1):47-102
We consider “hyperideal” circle patterns, i.e., patterns of disks appearing in the definition of the weighted Delaunay decomposition
associated with a set of disjoint disks, possibly with cone singularities at the centers of those disks. Hyperideal circle
patterns are associated with hyperideal hyperbolic polyhedra. We describe the possible intersection angles and singular curvatures
of those circle patterns on Euclidean or hyperbolic surfaces with cone singularities. This is related to results on the dihedral
angles of ideal or hyperideal hyperbolic polyhedra. The results presented here extend those in Schlenker (Math. Res. Lett.
12(1), 82–112, [2005]), however, the proof is completely different (and more intricate) since Schlenker (Math. Res. Lett.
12(1), 82–112, [2005]) used a shortcut which is not available here.
The author would like to thank the RIP program at Oberwolfach, where part of the research presented here was conducted. Partially
supported by the “ACI Jeunes Chercheurs” Métriques privilégiés sur les variétés à bord, 2003-06, and the ANR program Representations of surface groups, 2007-09. 相似文献
17.
M. Vanninathan 《Proceedings Mathematical Sciences》1981,90(3):239-271
In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of
the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic
expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we
denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet:
λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).
Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in
the case of Neumann eigenvalue problem. 相似文献
18.
E. V. Radkevich 《Journal of Mathematical Sciences》2006,133(1):1000-1044
The paper presents the regularization of the well-known Muskat problem based on the introduction of an order parameter describing
internal layers between two phases. The asymptotic solution is constructed, and its justification is given. The behavior of
the solution under the passage to the limit with respect the small parameter ε → 0 is studied.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial
Differential Equations, 2004. 相似文献
19.
Let X be a geodesic metric space. Gromov proved that there exists ε
0 > 0 such that if every sufficiently large triangle Δ satisfies the Rips condition with constant ε
0 · pr(Δ), where pr(Δ) is the perimeter of Δ, then X is hyperbolic. We give an elementary proof of this fact, also giving an estimate for ε
0. We also show that if all the triangles D í X{\Delta \subseteq X} satisfy the Rips condition with constant ε
0 · pr(Δ), then X is a real tree. Moreover, we point out how this characterization of hyperbolicity can be used to improve a result by Bonk,
and to provide an easy proof of the (well-known) fact that X is hyperbolic if and only if every asymptotic cone of X is a real tree. 相似文献
20.
G. A. Chechkin 《Journal of Mathematical Sciences》2006,135(6):3485-3521
We study the asymptotic behavior of eigenelements of boundary value problems in a domain Ω ⊂ ℝd, d ⩾ 3, with rapidly alternating type of boundary conditions. The density is equal to 1 outside tiny domains and is equal
to ε−m inside them, where ε is a small parameter. These domains (concentrated masses) of diameter εa are located on the boundary
at a positive distance of order O(ε) from each other, where a = const. The Dirichlet boundary condition is on parts of ∂Ω that are tangent to concentrated masses, and the Neumann boundary condition
is stated outside concentrated masses. We construct the limit (homogenized) operator, prove the convergence of eigenelements
of the original problem to the eigenelements of the limit (homogenized) problem in the case m ⩾ 2, and estimate the difference
between the eigenelements. Bibliography: 79 titles. Illustrations: 4 figures.
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Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 45–75. 相似文献