The fundamental properties of quasi-semigroups

[摘要] In this paper we focus on the abstract Cauchy problems of the time-dependent evolution equation = A(t)x(t). If the operator A(t) is time-independent, we can use the C0-semigroups theory to solve the abstract Cauchy problem. In this case A is a infinitesimal generator of the C0-semigroups. However, if A(t) is time-dependent, we can not apply directly the C0-semigroups theory to solve the problem. In this situation we can use the quasi semigroups theory as development of the two parameters semigroups. This semigroups is induced by bounded evolution operators U(t, s) that satisfy some assumptions. In this paper we determine the fundamental properties of the quasi semigroups included its generator related to the time-dependent evolution equation.

[发布机构] Mathematics Department, Universitas Gadjah Mada, Indonesia^1;Department of Mathematics Education, Universitas Sebelas Maret, Indonesia^2

[效力级别] 教育 [学科分类] 发展心理学和教育心理学

[关键词] Abstract Cauchy problem;Evolution operator;Fundamental properties;Infinitesimal generator;Time dependent;Time independents;Time-dependent evolutions;Two parameter