25 citations · 79 across the 8 of their papers we have counts for
8 papers
Exponential integrators for second-order in time partial differential equations
Alexander Ostermann, Duy Phan
Two types of second-order in time partial differential equations (PDEs), namely semilinear wave equations and semilinear beam equations are considered. To solve these equations wit…
A Reduced Order Controller for Output Tracking of a Kelvin-Voigt Beam
Lassi Paunonen, Duy Phan
We study output tracking and disturbance rejection for an Euler-Bernoulli beam with Kelvin-Voigt damping. The system has distributed control and pointwise observation. As our main…
Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems
Duy Phan, Lassi Paunonen
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential…
Reduced Order Controller Design for Robust Output Regulation
Lassi Paunonen, Duy Phan
We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show t…
Approximate controllability for Navier--Stokes equations in {\rm 3D} Cylinders under Lions boundary conditions by an explicit saturating set
Duy Phan
An explicit saturating set consisting of eigenfunctions of Stokes operator in general 3D Cylinders is proposed. The existence of saturating sets implies the approximate controllabi…
Approximate controllability for Navier--Stokes equations in rectangles under Lions boundary conditions
Duy Phan, Sérgio S. Rodrigues
The Navier--Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit satu…
Stabilization to trajectories for parabolic equations
Duy Phan, Sérgio S. Rodrigues
The feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain is addressed. The controls take values in a finite-dimensional s…
Gevrey regularity for Navier--Stokes equations under Lions boundary conditions
Duy Phan, Sérgio S. Rodrigues
The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and…