非线性反应扩散方程奇摄动问题

研究了具有非线性反应扩散方程奇摄动问题。在适当的条件下，利用微分不等式理论，讨论了当退化问题具有两个相交解时，原初始边值问题解的渐近性态。      

可加稳定过程的重点

本文研究了可加稳定过程的重点问题.利用自相交局部时计算可加稳定过程多重时的Hausdorff维数,证明了在适当条件下可加稳定过程重点的存在性.     

高校应用数学学报第18卷(2003年)B辑(英文版)第3期目次和提要

反应扩散方程的奇摄动莫嘉琪 (湖州师院 )　　王　辉 (国家自然科学基金委员会 )　　朱　江 (中国科学院大气物理研究所 )研究了一类反应扩散方程奇摄动初始边值问题 .在适当的条件下 ,利用微分不等式理论讨论了当退化问题具有两个相交解时 ,原初始边值问题解的渐近性态 .逼近严格伪压缩映象不动点的 Ishikawa迭代程序曾六川 (上海师范大学数学系 )设 X是一 Banach空间 ,K是 X的闭凸子集 ,T:K→ K是严格伪压缩的 Lipschitz映象 .文中证明了 T的任何不动点可用 Ishikawa迭代程序来范数逼近 ,还给出 Ishikawa迭代序列的收敛判据与收敛率…     

一类反应扩散方程奇摄动Robin问题的广义解

讨论了一类奇摄动反应扩散方程R ob in问题.在适当的条件下,研究了问题广义解的渐近性态.     

一类奇摄动反应扩散系统*

本文研究了一类奇摄动反应扩散系统的初始边值问题.在适当的条件下,利用比较定理讨论了问题解的渐近性态.     

一类非线性时滞反应扩散系统奇摄动问题

研究了一类具有非线性时滞反应扩散系统奇摄动问题.在适当的条件下,利用比较定理讨论了问题解的渐近性态.     

非局部反应扩散方程奇摄动问题

本文研究了一类具有非局部奇摄动反应扩散初始边值问题.在适当的条件下,利用比较定理讨论了问题解的渐近性态.     

一类具有摄动边界的弱非线性反应扩散方程

研究了具有摄动边界的非线性反应扩散方程的问题.在适当的条件下,利用微分不等式理论,讨论了问题的渐近解.     

反应扩散方程奇摄动Robin问题的渐近解

本文讨论了一类奇摄动反应扩散方程Robin问题,在适当的条件下,研究了问题渐近解的存在,唯一性及其渐近性态.     

具有边界摄动的非线性反应扩散方程奇摄动问题

研究了具有边界摄动的非线性反应扩散方程奇摄动问题．在适当的条件下,利用微分不等式理论,讨论了问题解的渐近性态．     

非退化扩散过程的极性与相交性

本文讨论非退化扩散过程的极性，得到了几个较好的充分条件，它可看作[1]的进一步深化，此外，我们将这些结果用来研究两个独立的非退化扩散过程的相交性，得到了一些有意思的结果。     

A NUMERICAL STUDY OF THE SPRUCE BUDWORM REACTION‐DIFFUSION EQUATION WITH HOSTILE BOUNDARIES

ABSTRACT. One of the interesting single species reaction diffusion problems is the spruce budworm model describing insect dispersal behavior. In an earlier study, Singh et al. [7] considered the two‐dimensional spruce budworm model with density dependent diffusion balanced by an artificial wind equal to the population gradient. Here we extend the model by considering more realistic density dependent diffusion and advection with hostile boundaries. We solve this model using a splitting method in which advection, diffusion and reaction processes are separated. Various hostility conditions have been used at the boundary. The numerical results show that the population moves quickly to a steady state outbreak situation when the advective components due to the density dependent diffusion are included.     

On conservativeness and recurrence criteria for Markov processes

In the present paper, we give general criteria of conservativeness and recurrence for Markov processes associated with, not necessarily symmetric, Dirichlet spaces. The conservativeness criterion is applied to discuss a comparison theorem of conservativeness for diffusion processes. Also some sufficient conditions of conservativeness and recurrence for diffusion processes.are given.     

UNSTEADY STATE DISPERSION OF AIR POLLUTANTS UNDER THE EFFECTS OF DELAYED AND NONDELAYED REMOVAL MECHANISMS

Abstract In this paper, we present a two‐dimensional time‐dependent mathematical model for studying the unsteady state dispersion of air pollutants emitted from an elevated line source in the atmosphere under the simultaneous effects of delayed (slow) and nondelayed (instantaneous) removal mechanisms. The wind speed and coefficient of diffusion are taken as functions of the vertical height above the ground. The deposition of pollutants on the absorptive ground and leakage into the atmosphere at the inversion layer are also included in the model by applying appropriate boundary conditions. The model is solved numerically by the fractional step method. The Lagrangian approach is used to solve the advection part, whereas the Eulerian finite difference scheme is applied to solve the part with the diffusion and removal processes. The solutions are analyzed to observe the effects of coexisting delayed and nondelayed removal mechanisms on overall dispersion. Comparison of delayed and nondelayed removal processes of equal capacity shows that the latter (nondelayed) process is more effective than the former (delayed removal) in the removal of pollutants from the atmosphere.     

Boundary conditions at a thin membrane for normal diffusion,classical subdiffusion,and slow subdiffusion processes

We consider three different diffusion processes in a system with a thin membrane: normal diffusion, classical subdiffusion, and slow subdiffusion. We conduct the considerations following the rule: If a diffusion equation is derived from a certain theoretical model, boundary conditions at a thin membrane should also be derived from this model with additional assumptions taking into account selective properties of the membrane. To derive diffusion equations and boundary conditions at a thin membrane, we use a particle random walk model in one-dimensional membrane system in which space and time variables are discrete. Then we move from discrete to continuous variables. We show that the boundary conditions depend on both selective properties of the membrane and a type of diffusion in the system.     

带干扰变破产限风险模型的破产概率

近年来,许多文献对经典风险模型及推广后的风险模型作了研究,并得出许多有用的结论.一般的文献都是假定保险公司的破产限为零.但在实际的保险业务中,当保险公司的盈余低于某一限度(破产限)时,保险公司就要调整政策或宣布破产.本文研究了带干扰的双Cox风险模型和带干扰的双Poisson风险模型在变破产限下的破产概率,得出了破产概率所满足的不等式,而且研究了当破产限为某一特殊函数时,破产概率所满足的不等式和具体的解析式.     

Dual ultracontractivity and its applications

The ultracontractivity is well studied and several equivalent conditions are known. In this paper, we introduce the dual notion of the ultracontractivity, which we call the dual ultracontractivity. We give necessary and sufficient conditions for the dual ultracontractivity. As an application, we discuss one-dimensional diffusion processes. We can write the conditions for the dual ultracontractivity in terms of speed measures.     

Variational formula for the stability of regime-switching diffusion processes

The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coeffcients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.     

带干扰风险模型中破产概率的Feller表示及可微性

给出带干扰风险模型中破产概率的Ｆｅｌｌｅｒ表示，并证明带干扰风险模型的破产概率的二次连续可微性。     

On transience of Lévy-type processes

In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called Lévy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the symbol of the corresponding pseudo-differential operator) for these properties, which are sharp for Lévy processes. Also, as a consequence, we discuss the weak and strong transience with respect to the dimension of the state space and Pruitt indices, thus generalizing some well-known results related to elliptic diffusion and stable Lévy processes. Finally, in the case when the symbol is radial (in the co-variable) we provide conditions for the weak and strong transience in terms of the Lévy measures.