Abstract Boundary Value Problems And Operator Semigroups

This thesis is divided into three parts. In the first character,two theorems about the unbounded perturbation of Hille — Yosida operator are proved,and with them we give two results on how to characterise the wellposedness of abstract boundary value problem with boundary perturbation.In the second character,we characterise the analyticity of abstract dynamic boundary value problem with unbounded boundary operator and abstract dynamic boundary value problem with bounded boundary operator using the decomposition of operator matrices.In the last character,the necessary and sufficient conditions for the positivity and stability of abstract dynamic boundary value problem are presented,which generalise some results in [5].As application,we discuss the positivity and stability of differential equation with delay.