可修复系统中具有耗散算子的抽象Cauchy问题解的适定性

The Well-posedness of Solution for the ACP with Dissipative Operator in Repairable System

摘要: 研究了耗散算子及其共轭算子的性质,给出了具有耗散算子的抽象Cauchy问题解的适定性条件,指出此类问题解的适定性与耗散算子的共轭算子的预解式存在与否密切相关.

Abstract: The properties of dissipative operator A and its conjugative operator A* are studied in this paper,and some sufficiency and necessity conditions of the well-posedness of solution for the ACP with operators A are obtained.These conditions are closely related with the existence of the R(λ;A*)=(λI-A*)-1.