Stefan－Signorini问题的均匀化

本文讨论了一维Ｓｔｅｆａｎ－Ｓｉｇｎｏｒｉｎｉ问题的均匀化．利用一个关于未知函数的变换，将原问题转化为一个等价问题，然后利用一些估计和分析技巧对后者进行均匀化．这部分地回答Ｊ．Ｒ．Ｒｏｄｒｉｓｕｅｓ提出的一个问题．     

A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.     

Quantization of Lie bialgebras,I

In the paper [Dr3] V. Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a quantization for Lie bialgebras, which arose from the problem of quantization of Poisson Lie groups. When the paper [KL] appeared Drinfeld asked whether the methods of [KL] could be useful for the problem of quantization of Lie bialgebras. This paper gives a positive answer to a number of Drinfeld's questions, using the methods and ideas of [KL]. In particular, we show the existence of a quantization for Lie bialgebras. The universality and functoriality properties of this quantization will be discussed in the second paper of this series. We plan to provide positive answers to most of the remaining questions in [Dr3] in the following papers of this series.     

The fluid flow through porous media. Regularity of the free surface

The fluid flow through an earth dam separating two water reservoirs of different levels gives rise to a free boundary problem. In [1] we have proved the existence of a solution to this problem. In this paper we show that the free boundary is regular.     

一类长波模型方程的解及其整体吸引子

本文使用细致的积分估计研究一类长波传播模型方程的整体解的存在唯一性及其渐近性态.全面改进[1]中的结果并是[2]中工作的深入.     

Existence and multiplicity of solutions for elliptic problems with indefinite discontinuous nonlinearities

In this paper we study the critical points for a locally Lipschitz functional that in some sense will be solutions of an elliptic problem with indefinite discontinuous nonlinearities. We should mention that our results were inspired by the work of Ambrosetti-Badiale [3], Arcoya-Calahorrano [5], Alama-Tarantello [1] and Chang [8]. For the problem studied in [3] we introduce indefinite nonlinearities as in [1] and [6]. To obtain the existence and multiplicity of solutions we use the critical points theory developed by Chang. Applications for Plasma Physics are considered with nonlinearities that change sign. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

拟线性正对称组具非线性特征的边值问题

谷超豪在[1]中就报告了拟线性正对称方程组边值问题解的存在和唯一性定理,详细的证明发表于[2],在[7]中对此有所改进,所建立的理论适用于非特征的齐次边值的情况。[3]参考了[2],[4]的做法,把[2]的结果推广到拟线性正对称组具某类特征的边值问题中去,但要求边界条件仍是齐次的。本文讨论边界条件是非齐次的,且是非线性的特征边值问题,在这种情况下建立了可微解的存在和唯一性定理。     

Spreading in space–time periodic media governed by a monostable equation with free boundaries,Part 2: Spreading speed

This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space–time periodic media. In Part 1 (see [2]) we have established a theory on the existence and uniqueness of solutions to this free boundary problem with continuous initial functions, as well as a spreading-vanishing dichotomy. We are now able to develop the methods of Weinberger [15], [16] and others [6], [7], [8], [9], [10] to prove the existence of asymptotic spreading speed when spreading happens, without knowing a priori the existence of the corresponding semi-wave solutions of the free boundary problem. This is a completely different approach from earlier works on the free boundary model, where the spreading speed is determined by firstly showing the existence of a corresponding semi-wave. Such a semi-wave appears difficult to obtain by the earlier approaches in the case of space–time periodic media considered in our work here.     

Exceptional Families and Existence Results for Nonlinear Complementarity Problem

In this paper we establish several sufficient conditions for the existence of a solution to the linear and some classes of nonlinear complementarity problems. These conditions involve a notion of the ``exceptional family of elements' introduced by Smith [19] and Isac, Bulavski and Kalashnikov [4], where the authors have shown that the nonexistence of the ``exceptional family of elements' implies solvability of the complementarity problem. In particular, we establish several sufficient conditions for the nonexistence as well as for the existence of the exceptional family of elements.     

An error analysis of the tau method for a class of singularly perturbed problems for differential equations

By using classical results of Poincaré and Birkhoff we discuss the existence and uniqueness of solution for a class of singularly perturbed problems for differential equations. The Tau method formulation of Ortiz [6] is applied to the construction of approximate solutions of these problems. Sharp error bounds are deduced. These error bounds are applied to the discussions of a model problem, a simple one-dimensional analogue of Navier-Stokes equation, which has been considered recently by several authors (see [2], [3], [8], [10]). Numerical results for this problem [8] show that the Tau method leads to more accurate approximations than specially designed finite difference or finite element schemes.     

Equilibrium problems with lower and upper bounds

In this paper, we obtain some existence results of equilibrium problems with lower and upper bounds by employing a fixed-point theorem due to Ansari and Yao [1] and Ky Fan Lemma [2], respectively. Our results give answers to the open problem raised by Isac, Sehgal and Singh [3].     

ON THE EXISTENCE OF SOLUTION OF A NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM ARISING FROM A LIQUID METAL FLOW

In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder＇s fixed-point theorem, we prove that the It improves the result of 0 ≤ Q 〈 1 in problem admits a solution for 0 ≤ Q ≤ 14.306 [2] and 0 ≤ Q ≤ 13.213 in [3].     

随机积分和微分方程解的存在性准则

在[1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

On generalized operator quasi-equilibrium problems

In this paper, we will introduce the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which generalize the operator equilibrium problem due to Kazmi and Raouf [K.R. Kazmi, A. Raouf, A class of operator equilibrium problems, J. Math. Anal. Appl. 308 (2005) 554-564] into multi-valued and quasi-equilibrium problems. Using a Fan-Browder type fixed point theorem in [S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994) 493-519] and an existence theorem of equilibrium for 1-person game in [X.-P. Ding, W.K. Kim, K.-K. Tan, Equilibria of non-compact generalized games with L^∗-majorized preferences, J. Math. Anal. Appl. 164 (1992) 508-517] as basic tools, we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which includes operator equilibrium problems.     

Banach空间中混合型微分─积分包含解的存在性

研究可分Ｂａｎａｃｈ空间中一类混合型的微分－积分包含，证明了解的存在性，其单值情形改进和推广了文［１～３］中关于混合型微分－积分方程的若干存在性结果．     

CONCERNING TIME-PERIODIC SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN CYLINDRICAL DOMAINS UNDER NAVIER BOUNDARY CONDITIONS

The problem of the existence of time-periodic flows in infinite cylindrical pipes in correspondence to any given, time-periodic, total flux, was solved only quite recently in [1]. In this last reference we solved the above problem for flows under the non-slip boundary condition as a corollary of a more general result. Here we want to show that the abstract theorem proved in [1] applies as well to the solutions of the well known slip (or Navier) boundary condition (1.7) or to the mixed boundary condition (1.14). Actually, the argument applies for solutions of many other boundary value problems. This paper is a continuation of reference [1], to which the reader is referred for some notation and results.     

一类非线性广义Euler-Poisson-Darboux方程整体解的渐近性质

J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.     

关于p－拉普拉斯方程径向解的一点注记

本文研究方程ｄｉｖ（｜ｕ｜ｐ－２ｕ）＋｜ｘ｜ｌ｜ｕ｜τ－１ｕ＝０，ｘ∈Ｂ的Ｄｉｒｉｃｈｌｅｔ边值问题ｕ｜Ｂ＝０的径向解。应用山路引理，我们将文［１］的结果（ｐ＝２时）推广到一般情形，证明上述问题有一非平凡的径向解。