Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup  

作　　者：GE ZhaoQiang FENG DeXing 

机构地区：[1]Department of Applied Mathematics, Xi’an Jiaotong University [2]Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Science

出　　处：《Science China(Information Sciences)》2013年第12期263-276,共14页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.61174081)

摘　　要：According to the well-posed problem of nonlinear singular distributed parameter systems, first of all, the nonlinear GE-semigroup induced by a continuous （possibly nonlinear） operator is introduced in Banach space, which is a generalization of GE-semigroup （i.e., generalized operator semigroup）, and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.According to the well-posed problem of nonlinear singular distributed parameter systems, first of all, the nonlinear GE-semigroup induced by a continuous （possibly nonlinear） operator is introduced in Banach space, which is a generalization of GE-semigroup （i.e., generalized operator semigroup）, and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.

关 键 词：nonlinear GE-semigroup nonlinear singular distributed parameter systems well-posed problem exponential stability Banach space 

分 类 号：O152.7[理学—数学] TP271.61[理学—基础数学]