In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett app...In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett approach,the solutions as a semigroup of non-linear operators.展开更多
This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The p...This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.展开更多
Consider the linear control systems x′(t)=Ax(t)+Bu(t)(t>0), x(0)=x_0 , where A is the generator of an exponentially stable C-semigroup on a Hilbert space X, B is a bounded operator from the Hilbert space Y to X. I...Consider the linear control systems x′(t)=Ax(t)+Bu(t)(t>0), x(0)=x_0 , where A is the generator of an exponentially stable C-semigroup on a Hilbert space X, B is a bounded operator from the Hilbert space Y to X. In the condition that the resolvent set A is not empty and the range of C is dense in X, we obtain that the extended controllability map is the unique self-adjoint solution to the Lyapunov equation. Moreover, sufficient conditions for asymptotically stability of C-semigroup are given.展开更多
文摘In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett approach,the solutions as a semigroup of non-linear operators.
文摘This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.
文摘Consider the linear control systems x′(t)=Ax(t)+Bu(t)(t>0), x(0)=x_0 , where A is the generator of an exponentially stable C-semigroup on a Hilbert space X, B is a bounded operator from the Hilbert space Y to X. In the condition that the resolvent set A is not empty and the range of C is dense in X, we obtain that the extended controllability map is the unique self-adjoint solution to the Lyapunov equation. Moreover, sufficient conditions for asymptotically stability of C-semigroup are given.
