局部n次积分C-半群与非齐次抽象Cauchy问题

Local n times integrated C-Semigroups and Inhomogeneous Abstract cauchy problem

作为强连续半群的推广,积分半群和C-半群进一步丰富了半群理论及应用,解决了强连续算子半群不能处理的某些不适定Cauchy问题。为了寻求积分半群对于解决非齐次抽象Cauchy问题的功效,选取了三类非齐次抽象Cauchy问题,给出了它们的解的定义,并在局部n次积分C-半群的概念和性质的基础上,证明了局部n次积分C-半群对于此类非齐次抽象Cauchy问题解的存在和唯一性条件。

Motivated by solving the ill-posed Cauchy problem about strongly continuous semigroups,two generalizations of strongly continuous semigroups,integrated semigroups and C-semigroups have enriched semigroups theory and application.In order to get the effect on solving inhomogeneous Abstract Cauchy problem by integrated semigroups,three classes of inhomogeneous Abstract Cauchy problems and their definitions of solutions are given.On the base of definiton and properties of local n times integrated C-semigroups,the conditions of the existence and uniqueness about the inhomogeneous Abstract Cauchy problem solution are obtained.