抽象发展方程非局部问题强解的存在性  

Existence of strong solutions for nonlocal problem of abstract evolution equations

作　　者：陈鹏玉[1] 高亚兵[1] 张旭萍[1,2] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070 [2]西北师范大学知行学院数学系,兰州730070

出　　处：《黑龙江大学自然科学学报》2016年第1期28-34,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11501455);甘肃省高等学校科研项目(2015A-003;2015A-213);西北师范大学青年教师科研能力提升计划资助项目(NWNU-LKQN-14-3)

摘　　要：在Hilbert空间框架下研究一类半线性发展方程非局部问题解的正则性,在非线性项满足次线性增长条件的情形下,运用解析半群理论及全连续算子的Leray-Schauder不动点定理,通过累次正则的方法,获得该问题强解的存在性。给出抛物型偏微分方程非局部问题的实例,说明所得抽象结果的可行性。The regularity of the solutions for nonlocal problem of a class of semilinear evolution equations is studied in a frame of Hilbert space.By applying the theory of analytic semigroups,Leray-Schauder fixed point theorem with respect to completely continuous operator and the method of iterated regular,the existence of strong solutions is obtained under sublinear growth condition of the nonlinear term.At last,an example of concrete parabolic partial differential equations with nonlocal conditions is also given to illustrate the feasibility of the obtained abstract results.

关 键 词：发展方程 非局部问题 解析半群 强解 存在性 

分 类 号：O175.8[理学—数学]