Seminar: On a New Perturbation Theory of $C_0$-semigroups

Thời gian: 09:30 đến 11:30 Ngày 25/03/2026

Địa điểm: Phòng C101, VIASM

Báo cáo viên: Nguyễn Văn Minh, University of Arkansas at Little Rock, USA

Tóm tắt: This talk is concerned with some development of a new perturbation theory for $C_0$-semigroups in Banach spaces. Given a $C_0$-semigroup $\left (T(t)\right )_{t\ge 0}$ with $\| T(t)\| \le Me^{\omega_0 t}$, $t\ge 0$, in a Banach space $\mathbb{X}$ with generator $A$, it is of interest to many mathematicians to know when the perturbed operator $A+B$ also generates a $C_0$-semigroup. This is a classical problem in the theory of $C_0$-semigroups with applications to PDE or FDE, especially when the perturbation $B$ is an unbounded operator in the space $\mathbb X$. Many results as answers to this question were obtained, including our recent one $$ \sup_{\mu >\omega_0 } \| (\mu-\omega_0) BR(\mu,A)\| <\infty . $$ In this talk we will give some updates about our joint work (with Dr Xuan-Quang Bui, Vu Trong Luong and Nguyen Duc Huy) on this problem as well as further investigation in the case the perturbation depending on time $t$.