具非线性耗散项P系统的Cauchy问题

讨论具有非线性耗散项P系统的Caucby问题．在一些较为合理的假设下．证明了其光滑解的整体存在性及其解的奇性形成．     

具耗散项拟线性双曲型方程组的边值问题

本文考虑具耗散项一阶拟线性双曲型方程组的具有自由边界的典型自由边值问题．在一些合理假设下,证明了其经典解的整体存在性定理．     

Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms

Abstract In this paper, the author studies the global existence, singularities and life span of smoothsolutions of the Cauchy probleth for a class of quasilinear hypetbolic systems with higher order dissipativeterms and gives their applications to nonlinear wave equations with higher order dissipative terms.     

Asymptotic Decay for Some Differential Systems with Fading Memory

We study the large time behavior of the solution u to an initial and boundary value problem related to the following integro-differential equation $$ u_{tt} = G_0 \Delta u + \int_0^t G'(t-s) \Delta u(x, s)\, ds - a u_t \eqno(0.1) $$ where G 0 , a are real constant coefficients, G 0 > 0, a S 0 and $ G\,' \in L^1({{\shadR}}^ + ) \cap L^2({{\shadR}}^ + ), G\,' \le 0 $ . It is known that, when G ' L 0 and a > 0, the solution u of (0.1) exponentially decays. Here we prove that, for any nonnegative a and for any $ G ' \not \equiv 0 $ , the solution u of the Eq. (0.1) exponentially decays only if the relaxation kernel G ' does. In other words, the introduction of the dissipative term related to G ' does not allow the exponential decay due to the presence of the positive coefficient a . We also prove analogous results for the polynomial decay.     

On the Decay of Solutions for Some Nonlinear Dissipative Hyperbolic Equations

In this paper we show the decay of solutions to the initial-boundary value problem for somenonlinear hyperbolic equation with a nonlinear dissipative term,by using a difference inequality.     

A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

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T-IPH分布的若干性质及其在排队论中的应用

本文讨论T-IPH分布的一些重要性质,其中T-IPH表示可数状态离散时间吸收生灭链吸收时间的分布.对该分布,首先给出了其概率生成函数(PGF),在此基础上,进~步给出了计算分布概率分布律以及阶乘矩数值结果的迭代公式.另外,还讨论了T-IPH分布在排队论中的一个应用.     

Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems

This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that general weighted integral inequalities together with convexity arguments allow us to produce a general semi-explicit formula which leads to decay rates of the energy in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We also give three other significant examples of nonpolynomial growth at the origin. Our work completes the work of [15] and improves the results of [21] and [22] (see also [23] and [10]). We also prove the optimality of our results for the one-dimensional wave equation with nonlinear boundary dissipation. The key property for obtaining our general energy decay formula is the understanding between convexity properties of an explicit function connected to the feedback and the dissipation of energy.     

Formation of Singularities of Solutions for Cauchy Problem of Quasilinear Hyperbolic Systems with Dissipative Terms

ln this paper, for a class of 2 × 2 quasilinear hyperbolic systems, we get existence theorems of the global smooth solutions of its Cauchy problem, under a certain hypotheses. In addition, Tor two concrete quasilinear hyperbolic systems, we study the formation of the singularities of the C¹-solution to its Cauchy problem.     

On the Applications of the Frequency-Domain Method for Uniformly Dissipative Non-Linear Systems

In this paper, we introduce the idea of dual systems of the frequency-domain method for uniform dissipativity. We prove the equivalence of the frequency-domain conditions for dual systems and apply it to a third-order non-linear differential equation arising from the vacuum tube circuit problem studied by Rauch [8]. An earlier result of BARBALAT and HALANAY [5] is obtained as a particular case.     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

Global Classical Solutions for One Dimensional Hydromagnetic Ow with Dissipative Terms

This paper concerned with the classical solutions to system of one dimensional hydromagnetic dynamics with dissipative mechanism. Under certain hypotheses on the initial data, the global existence and the formation of singularities for classical solution are obtained. Our results show that the damping dissipation is strong enough to preserve the smoothness of the classical solution.     

Decay of Dissipative Equations and Negative Sobolev Spaces

We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.     

Infinite-Dimensional Hamiltonian and Lagrangian Systems with Constraints

Mathematical Notes -     

实数若干性质的证明及其应用

本文介绍实数的阿基米德性、稠密性等性质的证明及其应用,同时也推广了已有文献的相关结论.     

Data Sphering: Some Properties and Applications

Centring-then-sphering is a very important pretreatment in data analysis. The purpose of this paper is to study the asymptotic behavior of the sphering matrix based on the square root decomposition (SRD for short) and its applications. A sufficient condition is given under which SRD has nondegenerate asymptotic distribution. As examples, some commonly used and affine equivariant estimates of the dispersion matrix are shown to satisfy this condition. The case when the population dispersion matrix varies is also treated. Applications to projection pursuit (PP) are presented. It is shown that for elliptically symmetric distributions the PP index after centring-then-sphering is independent of the underlying population location and dispersion.     

Cantor集的性质及应用

Cantor集是实函数论中一类重要的集合.本文从定义、性质及应用三方面研究了Cantor集.目的是帮助初学者对Cantor集有一个较全面的认识.     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.