一类非线性微分方程的脉冲镇定

针对一般形式的常微分系统提出了脉冲指数镇定的概念，具体研究了一类分离变量型非线性常微分方程的脉冲镇定问题，得到了该方程可脉冲指数镇定的充分判据，全文的概念及结论突出了脉冲在方程稳定性方面的控制效果。     

Regularity and convergence of stochastic convolutions in duals of nuclear Fréchet spaces

Let Φ′ be the strong dual of a nuclear Fréchet space Φ. In this paper we present regularity properties, weak convergence, and convergence in probability and in mean square of Φ′-valued stochastic evolution equations and convolutions with respect to Φ′-valued cadlag martingales.     

拟线性抛物型方程广义解的局部有界性

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.     

Sharp global well-posedness for KdV and modified KdV on

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all -based Sobolev spaces where local well-posedness is presently known, apart from the endpoint for mKdV and the endpoint for KdV. The result for KdV relies on a new method for constructing almost conserved quantities using multilinear harmonic analysis and the available local-in-time theory. Miura's transformation is used to show that global well-posedness of modified KdV is implied by global well-posedness of the standard KdV equation.

     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

关于Logistic模型的倍周期收敛现象

运用实验和归纳的方法 ,讨论了如何利用 Mathematic数学软件观察 Logistic模型的倍周期收敛现象以及对初值的依赖性 ,并从理论上解释了倍周期收敛现象     

Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.Centro de Investigación y de Estudios Avanzados.