一类反应扩散过程的无穷小算子在Banach和Hilbert空间的有界性  

The boundary of a class of infinitesimal operators of reaction and diffusion process in Hilbert and Banach space

作　　者：郑晓阳[1] 徐润章[1] 于涛[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2004年第4期550-552,共3页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(10271034);哈尔滨工程大学基础研究基金资助项目(HEUF04012;04022).

摘　　要：反应扩散过程是研究反应扩散现象的2种基本方法之一.而反应扩散过程的定义和性质也依赖于其无穷小算子的性质.定义了一类新的反应扩散过程的无穷小算子,得到了有关此类无穷小算子的性质.并证明了其在Ba nach和Hilbert空间上的有界性,以及相应的矩的有限性.目的在于进一步讨论反应扩散过程的性质.使用的主要方法为将反应扩散过程的无穷小算子定义于Banach空间和Hilbert空间之中,通过对无穷小算子Ω的共轭算子Ω 的研究,得出Ω的有关性质,主要工具为Gronwall不等式和一些泛函分析的工具.主要结果为Ω (x)≤b+d+n2(M+1)Dx及ExXt≤X0e(b+d+n2(M+1)D)t,这里b,d和n为无穷小算子的定义中的参数.The reaction and diffusion process is one of two basic ways of studying the phenomenon of the reaction and diffusion .The definition and characteristics of the reaction and diffusion process were proven depended on infinitesimal operators. After defining a class of the new infinitesimal operators on the reaction and diffusion process and their characteristics,the boundary of the class of infinitesimal operators of reaction and diffusion process was proven in the space of Hilbert and Banach. The moments were found to be finite. The main method is applied to Ω~ which is the conjugate operator of Ω in order to get the characteristics of Ω.The main tools are Gronwall inequality and other functional analysis tools. The main results of this paper are Ω~(x)≤b+d+n^2(M+1)Dx and ExXt≤X0e^((b+d+n^2(M+1)D)t),where b,d,n　are parameters in the definition of infinitesimal operators.

关 键 词：反应扩散过程 无穷小算子 有界性 矩 

分 类 号：O211.6[理学—概率论与数理统计]