4 papers
On the well-posedness of linear evolution equations under unbounded nonautonomous perturbations
Xuan-Quang Bui, Vu Trong Luong, Nguyen Van Minh
We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where generates a $\mat…
A generation theorem for the perturbation of strongly continuous semigroups by unbounded operators
Xuan-Quang Bui, Nguyen Duc Huy, Vu Trong Luong +1
In this paper we study the well-posedness of the evolution equation of the form , , where is the generator of a - semigroup and is a (possib…
Roughness of exponential dichotomy under unbounded perturbation in linear partial functional differential equations
Xuan-Quang Bui, Nguyen Van Minh
This paper is concerned with the roughness of exponential dichotomies under unbounded perturbations of a class of linear partial functional differential equations \begin{equation}\…
Yosida Distance and Existence of Invariant Manifolds in the Infinite-Dimensional Dynamical Systems
Xuan-Quang Bui, Nguyen Van Minh
We introduce a new concept of Yosida distance between two (unbounded) linear operators and in a Banach space defined as $d_Y(A,B):=\limsup_{μ\to +\infty} \| A_…