The Inhomogeneous Neumann Problem in Lipschitz Domains

Abstract

Existence and uniqueness is established for the solution to the inhomogeneous Neumann problem for Laplace's equation in Lipschitz domains with data in L ^P Sobolev spaces.     

Supercritical Spatially Homogeneous Branching in Admits no Equilibria

At the beginning of investigations in spatially homogeneous branching processes in Euclidean space (Liemant [1]) it seemed to be obvious that the existence of equilibria implies criticality of branching. This prejudice was disproved by the example [2] of a subcritical homogeneous branching equilibrium in dimension one. We prove that supercritical homogeneous branching processes in Euclidean space and, more general, in a broad class of topological groups have no (non – void, homogeneous) equilibria.     

On Persistence and Stability of Some Spatially Inhomogeneous Systems

Local and global stability and persistence of some coupled map lattices (CMLs) and partial differential equations are studied. A logistic CML with noninteger time step and delay is introduced. The persistence results for reaction-diffusion equations are extendable to the telegraph reaction-diffusion equation for a sufficiently small delay parameter. The stability and persistence results are applied to ecology, physics, economics, and immunology.     

Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains

In this paper, firstly we give an atomic decomposition of the local Hardy spaces h^p_r(Ω)(O < p ≤ 1) and their dual spaces. where the domain Ω is exterior regular in R^n(n ≥ 3). Then for given data f ∈ h^p_r(Ω), we discuss the inhomogeneous Dirichlet problems: {Lu = f \quad in Ω u = 0 \qquad on ∂ Ω where the operator L is uniformly elliptic. Also we obtain the estimation of Green potential in the local Hardy spaces h^p_r(Ω).     

Wandering Domains in Non-Archimedean Polynomial Dynamics

We extend a recent result on the existence of wandering domainsof polynomial functions defined over the p-adic field C_p toany algebraically closed complete non-archimedean field C_K withresidue characteristic p > 0. We also prove that polynomialswith wandering domains form a dense subset of a certain one-dimensionalfamily of degree p + 1 polynomials in C_K[Z]. 2000 MathematicsSubject Classification 12J25 (primary), 37F99 (secondary).     

Spatially Inhomogeneous Populations with Seed-Banks: I. Duality,Existence and Clustering

Journal of Theoretical Probability - We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are...     

二维Lipschitz区域上一类带L^p边值的非齐次多调和Neumann问题

该文运用层位势方法研究了二维Lipschitz区域上一类带L^p边值的非齐次多调和Neumann问题.利用多层S位势,给出了该类问题的惟一积分表示解,其中,多层S位势是经典单层位势的高阶类似物,通过多调和基本解加以定义.     

Convergence to Global Equilibrium for Spatially Inhomogeneous Kinetic Models of Non-Micro-Reversible Processes

We study the long-time asymptotics of linear kinetic models with periodic boundary conditions or in a rectangular box with specular reflection boundary conditions. An entropy dissipation approach is used to prove decay to the global equilibrium under some additional assumptions on the equilibrium distribution of the mass preserving scattering operator. We prove convergence at an algebraic rate depending on the smoothness of the solution. This result is compared to the optimal result derived by spectral methods in a simple one dimensional example.     

p-Adic Dynamics and Sullivan's No Wandering Domains Theorem

In this paper we study dynamics on the Fatou set of a rational function . Using a notion of components of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points.     

Dynamics of Inhomogeneous Chains of Coupled Quadratic Maps

A new effective local analysis method is elaborated for coupled map dynamics. In contrast to the previously suggested methods, it allows visually investigating the evolution of synchronization and complex-behavior domains for a distributed medium described by a set of maps. The efficiency of the method is demonstrated with examples of ring and flow models of diffusively coupled quadratic maps. An analysis of a ring chain in the presence of space defects reveals some new global-behavior phenomena.     

空间弹性变形梁动力学的旋量系统理论方法

所谓空间弹性梁,即同时考虑受弯曲、拉伸和扭转等力作用而发生空间变形的梁.借助于刚体运动的旋量理论,引入了"变形旋量"这一概念,进而提出了空间弹性梁的旋量理论.在基本的运动学假设和材料力学理论基础上,分析并给出了梁的空间柔度.接着研究了空间弹性梁的动力学,用旋量理论分析了其动能和势能,从而得到了Lagrange算子.通过对边界条件和变形函数的讨论,进一步运用Rayleigh-Ritz方法计算了系统的振动频率.将空间弹性梁与纯弯曲、扭转或者拉伸等简单变形情况下的特征频率做了对比研究.最后,运用所提出的空间弹性梁理论研究了一关节轴线互相垂直的两空间柔性杆机械臂的动力学,通过动力学仿真发现了关节的刚性运动和空间柔性杆的弹性变形运动之间的耦合影响.该文的研究工作阐明了运用旋量系统理论解决具有空间弹性变形杆件的机构动力学问题的有效性.     

Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

We introduce a new mean field kinetic model for systems of rational agents interacting in a game-theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.     

On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.     

Problems on Time-Varying Domains: Formulation,Dynamics, and Challenges

Acta Applicandae Mathematicae - The purpose of this article is to introduce the reader to phenomena on time-varying spatial domains and to highlight the differences from their counterpart on...     

Dynamics of Spatially Distributed Chains of Coupled Systems of Equations in a Two-Dimensional Domain

Mathematical Notes - The local dynamics of coupled identical nonlinear systems of second-order differential equations in a two-dimensional domain is studied. The main assumption is that the number...     

超连续Domain与拟超连续Domian

讨论了超连续domain与拟超连续domain的相关性质,证明了超连续半格范畴为有性质M*的拟超连续domain范畴的反射子范畴。     

Lip_J-扩张域和一致域(英文)

本文证明了如下两个结果:(1)域D(?)R~n是一致域当且仅当D是Lip_J-扩张域;(2)Jordan域D(?)R~2是拟圆当且仅当对在D上满足|f′(z)|≤d(z,(?)D)~(-1)的任意的解析函数f恒有f∈Lip_J(D),其中J(x_1,x_2)=1/2 log(1+|x_1-x_2|/d(x_1,(?)D))(1+|x_1-x_2|/d(x_2,(?)D)),x_1,x_2∈D.