Searcharxiv⌕ Search

arXiv subjects

Duc-Trung Hoang

Publications and source records attributed to Duc-Trung Hoang.

5 recordsLinked to original sources
arXiv2018

Controllability and observability for non-autonomous evolution equations: the averaged Hautus test

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact observability. Next, we extend this to more general class of operators under a growth condition on the associated evolution family. We give an application to the Schrödinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient.

math.AP↗
arXiv2018

Observability of a 1D Schrödinger equation with time-varying boundaries

We discuss the observability of a one-dimensional Schrödinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we provide exact boundary observability when the curve satisfies some certain conditions . By duality theory, we establish the controllability of adjoint system.

math.OC↗
arXiv2017

Exact observability of a 1D wave equation on a non-cylindrical domain

We discuss admissibility and exact observability estimates of boundary observation and interior point observation of a one-dimensional wave equation on a time dependent domain for sufficiently regular boundary functions. We also discuss moving observers inside the non-cylindrical domain and simultaneous observability results.

math.AP↗