8 papers
Rapid stabilization for Stokes and Navier-Stokes systems with localized disturbance
Christian Calle, Patricio Guzmán, Hugo Parada +1
In this study, we analyze the rapid stabilization of Stokes and the two- and three-dimensional Navier-Stokes systems in the presence of an unknown spatially localized disturbance.…
Optimal stabilization rate for the wave equation with hyperbolic boundary condition
Hugo Parada, Nicolas Vanspranghe
We show that the energy of classical solutions to the wave equation with hyperbolic boundary condition (i.e., dynamic Wentzell boundary condition) and damping on the boundary decay…
Rapid stabilization of the heat equation with localized disturbance
Patricio Guzmán, Hugo Parada, Christian Calle-Cárdenas
This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control s…
Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls
Patricio Guzmán, Felipe Labra, Hugo Parada
In this work, we analyze the internal and boundary stabilization of the Cahn-Hilliard and Kuramoto-Sivashinsky equations under saturated feedback control. We conduct our study thro…
A Nonhomogeneous Boundary-Value Problem For The Nonlinear KdV Equation on Star Graphs
Roberto de A. Capistrano Filho, Hugo Parada, Jandeilson Santos da Silva
This paper investigates an initial-boundary value problem for the Korteweg--de Vries (KdV) equation on a finite equilateral star graph. We use the notion of -compatibility, whic…
Rapid stabilization for a wave equation with boundary disturbance
Patricio Guzmán, Agustín Huerta, Hugo Parada
In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundar…
Spectral scheme for an energetic Fokker-Planck equation with -distribution steady states
Claudia Negulescu, Hugo Parada
The concern of the present paper is the design of efficient numerical schemes for a specific Fokker-Planck equation describing the dynamics of energetic particles occurring in ther…
An analysis of the entire functions associated with the operator of the KdV equation
Roberto de A. Capistrano Filho, Hugo Parada, Jandeilson Santos da Silva
It is well known that the controllability property of partial differential equations (PDEs) is closely linked to the proof of an observability inequality for the adjoint system, wh…