Well-posedness of two classes of singular distributed parameter systems in Hilbert space

Abstract

One of the most important problems for the study of singular distributed parameter systems is the well-posedness. Not only is it very important for the study of stability of singular distributed parameter systems, but also it is the theoretic basis for the study of the related problem of optimal control. In this paper, the concepts and the properties of generalized operator semigroup(GOS) and generalized integral semigroup(GIS) are given in Hilbert space, the solving problem of the nonhomogeneous singular distributed parameter system is discussed by the concepts and the properties of GOS and GIS in Hilbert space, and some important results of the two classes of singular distributed parameter systems are given. ©2010 IEEE.