具有源项的等熵气体动力学方程组全局解的存在性

本文我们证明了具有源项的等熵气体动力学方程组(1.2)全局解的存在性.为此,我们构造正则双曲方程组(1.1)去逼近非齐次等熵气体动力学方程组(1.2).首先,对每一个固定的逼近参数δ和一般化的P(ρ)条件,我们证明了带有界初始条件(1.4)的Cauchy问题(1.1)的全局熵解的存在性.其次,令∈=o(δ),我们得到了方程组(1.2)的形如η(ρ,u)=ρH(ρ,u)(与Chen和LeFloch(2003)相同)的弱熵对的H_(loc)~(-1)紧性的完整证明.最后,将Chen和LeFloch(2003)给出的关于P(ρ)的条件应用到定理1和定理2的结果中,我们得到了带有界初值(1.4)的Cauchy问题(1.2)的熵解的全局存在性.     

广义集值强非线性混合似变分不等式解的迭代逼近

延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式．证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性．利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法,最终证明了这类广义强非线性混合似变分不等式解的存在性及由算法生成的迭代序列的收敛性．     

关于非齐次柯西问题的强解

利用自反Banach空间中弱紧算子的因子分解技巧，对于一类非齐次项具有连续Lipschitz扰动的柯西问题，当其齐次项算子生成强连续算子半群且具有紧豫解式限制时，证明了方程强解的存在性．     

一类非齐次弹性力学方程组整体熵解的存在性

考虑非线性、非齐次弹性力学方程组在一定条件下整体熵解的存在性问题.由不变区域理论导出粘性解的L~∞模的先验估计,利用粘性消失法结合补偿列紧理论给出粘性解的收敛性,即广义解的存在性.     

带有退化强制项的非线性椭圆方程解的存在性与不存在性

本文研究带有退化强制主部算子的非线性椭圆型方程解的存在性与不存在性.对于外力项为可积函数的情形,首先对方程进行适当的光滑逼近并得到逼近方程有界弱解的存在性,随后通过选取适当的试验函数,结合非线性项的增长次数建立逼近解的一致正则性估计,进而利用适当的紧性定理给出逼近解序列的收敛性,从而得到方程有限能量弱解的存在性;对于外力项为奇异Radon测度的情形,我们结合适当的测度分解技巧与逼近解的收敛性证明熵解的不存在性.     

非自治Klein-Gordon-Schr(o)dinger格点动力系统的一致吸引子

首先证明了耗散的非自治Klein-Gordon-Schr(o)dinger格点动力系统的解确定的一族过程的紧一致吸引子的存在性.其次得到了该紧一致吸引子的Kolmogorov熵的一个上界.最后建立了该紧一致吸引子的上半连续性.     

非线性抛物问题熵解的某些定性性质

本文研究了非线性抛物问题熵解的正性依赖于初始资料和方程右端项的正性以及熵解的稳定性依赖于方程右端项的弱 Ｌ~１摄动．     

补偿紧性在奇异四阶和六阶摄动偏微分方程中的应用

在这篇文章中，我们应用补偿紧性方法，能量方法得到了一类四阶、六阶奇异摄动微分方程解的收敛性问题，并进一步提高了解的正则性．     

具变动控制结构的对称广义强向量拟均衡问题及其应用

讨论了具变动控制结构的对称广义强向量拟均衡问题.在锥值映射具无限上连续性条件下,利用Fan-KKM定理和Kakutani-Fan-Glicksberg不动点定理,建立了解的存在性结果,进一步,还得出了其解集的紧性结论.作为应用,文中还给出了广义强向量拟鞍点问题解的存在性及其解集的紧性结果.这些结果推广和发展了近期已有文献的相关结论.     

BANACH空间中二阶脉冲积分-微分方程初值问题的解

在较弱的条件下,我们研究了Banach空间中二阶脉冲积分-微分方程初值问题解的存在性,建立了解的存在定理,本质地改进了郭大钧的相关结果．同时,利用非紧性测度还给出了存在最大最小解的一个充分条件．     

Homogeneous weak solenoids

A (generalized) weak solenoid is an inverse limit space over manifolds with bonding maps that are covering maps. If the covering maps are regular, then we call the inverse limit space a strong solenoid. By a theorem of M.C. McCord, strong solenoids are homogeneous. We show conversely that homogeneous weak solenoids are topologically equivalent to strong solenoids. We also give an example of a weak solenoid that has simply connected path-components, but which is not homogeneous.

     

多目标规划的 Lagrange 对偶与标量化定理

定义与问题设 K(?)R~p 为内部非空的点锥,则 K 在 R~p 上确定了如下偏序:x≦K.y(?)y-x∈K,xk(?)}.     

Entropies and weak solutions of the compressible isentropic Euler equations

In this Note, we study the system of isentropic Euler equations for compressible fluids, with a general equation of state. We establish the existence of the fundamental kernel that generates the family of weak entropies, and study its singularities. The kernel is the solution of an equation of Euler-Poisson-Darboux type, and its partial derivative with respect to the density variable tends to a Dirac measure as the density approaches zero. We prove a new reduction theorem for the Young measures associated with the compressible Euler system. From these results, we deduce the existence, compactness, and asymptotic decay of measurable and bounded entropy solutions.     

On the theorem of T. Yamada and S. Watanabe

The well-known theorem of T. Yamada and S. Watanabe asserts that (weak) existence and pathwise uniqueness of the solution of a stochastic equation implies the existence of a strong solution. This is the most powerful tool for proving that a stochastic equation possesses a strong solution. However, pathwise uniqueness is far from being a necessary condition for this. Even if the solution is not unique in law it is also of interest to ask for strong solutions. In the present note, we will discuss in more detail the connection between pathwise uniqueness and the existence of a strong solution. We will state a condition which is not only sufficient but also necessary for the existence of a strong solution.     

Existence theorems for generalized vector variational inequalities with a variable ordering relation

In this paper we study the solvability of the generalized vector variational inequality problem, the GVVI problem, with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVVIs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVVI problems without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.     

Iterative solutions of the split common fixed point problem for strictly pseudo-contractive mappings

In this paper, we study the the split common fixed point problem in Hilbert spaces. We establish a weak convergence theorem for the method recently introduced by Wang, which extends a existing result from firmly nonexpansive mappings to strictly pseudo-contractive mappings. Moreover, our condition that guarantees the weak convergence is much weaker than that of Wang’s. A strong convergence theorem is also obtained under some additional conditions. As an application, we obtain several new methods for solving various split inverse problems and split equality problems. Numerical examples are included to illustrate the applications in signal processing of the proposed algorithm.     

Some Existence Results for Vector Quasivariational Inequalities Involving Multifunctions and Applications to Traffic Equilibrium Problems

Some existence results for vector quasivariational inequalities with multifunctions in Banach spaces are derived by employing the KKM-Fan theorem. In particular, we generalize a result by Lin, Yang and Yao, and avoid monotonicity assumptions. We also consider a new quasivariational inequality problem and propose notions of weak and strong equilibria while applying the results to traffic network problems.     

On F-Implicit Generalized Vector Variational Inequalities

In this paper, we study the F-implicit generalized (weak) case for vector variational inequalities in real topological vector spaces. Both weak and strong solutions are considered. These two sets of solutions coincide whenever the mapping T is single-valued, but not set-valued. We use the Ferro minimax theorem to discuss the existence of strong solutions for F-implicit generalized vector variational inequalities.     

Analysis and numerical simulation for a class of time fractional diffusion equation via tension spline

In this work, we prove the weak and strong convergence of a sequence generated by a modified S-iteration process for finding a common fixed point of two G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. We also give some numerical examples for supporting our main theorem and compare convergence rate between the studied iteration and the Ishikawa iteration.     

A General Darling–Erdős Theorem in Euclidean Space

We provide an improved version of the Darling–Erd?s theorem for sums of i.i.d. random variables with mean zero and finite variance. We extend this result to multidimensional random vectors. Our proof is based on a new strong invariance principle in this setting which has other applications as well such as an integral test refinement of the multidimensional Hartman–Wintner LIL. We also identify a borderline situation where one has weak convergence to a shifted version of the standard limiting distribution in the classical Darling–Erd?s theorem.