V. Luong

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20242026

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math.DS2026

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 $A$ generates a $\mat…

math.DS2024

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 $u^{'} (t) = A u (t) + C u (t)$ , $t \geq 0$ , where $A$ is the generator of a $C_{0}$ - semigroup and $C$ is a (possib…

math.DS2024

Existence of bounded asymptotic solutions of autonomous differential equations

Vu Trong Luong, William Barker, Nguyen Duc Huy +1

We study the existence of bounded asymptotic mild solutions to evolution equations of the form $u^{'} (t) = A u (t) + f (t), t \geq 0$ in a Banach space $\X$, where $A$ generates an (analytic)…