抽象半线性发展方程初值问题解的存在性  

Existence of Solutions of Initial Value Problems for Abstract Semilinear Evolution Equations

作　　者：李永祥[1] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070

出　　处：《数学学报（中文版）》2005年第6期1089-1094,共6页Acta Mathematica Sinica：Chinese Series

基　　金：甘肃省自然科学基金(ZS031-A25-003-Z)NWNU-KJCXGC-212基金

摘　　要：本文研究Banach空间E中具有非紧半群的半线性发展方程初值问题u′(t)+Au(t)=f(t,u(t)),t≥0;u(0)=x_0解的存在性,其中-A为E中等度连续C_0-半群的生成元,f:[0,∞)×E→E连续。在f满足较弱的非紧性测度条件下,获得了该问题饱和mild解的存在性。特别,当E为有序弱序列完备Banach空间时,我们获得了一个不需要非紧性测度条件的便于应用的存在性结果。This paper discusses the existence of solutions of initial value problem for semilinear evolution equation with noncompact semigroup u＇（t）＋Au（t） = f（t, u（t））, t≥ 0; u（0） = x0 in a Banach space E, where -A is the infinitesimal generator of an equicontinuous Co -semigroup, and f ： [0,∞）×E→ E is continuous. In the case where f satisfies a weaker noncompactness measure condition, the existence results of saturated mild solutions are obtained. Particularly, an existence result without using noncompactness measure condition is present in ordereded and weakly sequentially complete Banach spaces. This result is very convenient for application.

关 键 词：抽象发展方程 G0-半群 存在性 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]