16 citations · 44 across the 20 of their papers we have counts for
21 papers
Control of Kawahara equation using flat outputs
Roberto de A. Capistrano-Filho, Jandeilson Santos da Silva
In this study we focused on the linear Kawahara equation in a bounded domain, employing two boundary controls. The controllability of this system has been previously demonstrated o…
Control of the Schrödinger equation in : The critical case
Pablo Braz e Silva, Roberto de A. Capistrano-Filho, Jackellyny Dassy do Nascimento Carvalho +1
This article deals with the --level local null controllability for the energy-critical nonlinear Schrödinger equation in . Firstly, we demonstrate that the pro…
Observability of the linear Zakharov--Kuznetsov equation
Roberto de A. Capistrano Filho, Vilmos Komornik, Ademir F. Pazoto
We study the linear Zakharov--Kuznetsov equation with periodic boundary conditions. Employing some tools from the nonharmonic Fourier series we obtain several internal observabilit…
Boundary controllability of the Korteweg-de Vries equation: The Neumann case
R. de A. Capistrano-Filho, J. S. da Silva
This article gives a necessary first step to understanding the critical set phenomenon for the Korteweg-de Vries (KdV) equation posed on interval considering the Neumann bo…
Coupled linear Schrödinger equations: Control and stabilization results
K. Bhandari, R. de A. Capistrano-Filho, S. Majumdar +1
This article presents some controllability and stabilization results for a system of two coupled linear Schrödinger equations in the one-dimensional case where the state components…
Stability of solitary waves for generalized -Boussinesq system: The Hamiltonian case
Roberto de A. Capistrano Filho, Jose Raul Quintero, Shu-Ming Sun
The -Boussinesq system is a model of two equations that can describe the propagation of small-amplitude long waves in both directions in the water of finite depth. Considerin…
On the boundary stabilization of the KdV-KdV system with time-dependent delay
Roberto de A. Capistrano-Filho, Boumediène Chentouf, Victor H. Gonzalez Martinez +1
The boundary stabilization problem of the Boussinesq KdV-KdV type system is investigated in this paper. An appropriate boundary feedback law consisting of a linear combination of a…
A qualitative study of the generalized dispersive systems with time-delay: The unbounded case
Roberto de A. Capistrano Filho, Fernando Gallego, Vilmos Komornik
We study the asymptotic behavior of the solutions of the time-delayed higher-order dispersive nonlinear differential equation \begin{equation*} u_t(x,t)+Au(x,t) +λ_0(x) u(x,t)+λ(x)…
Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback
Roberto de A. Capistrano-Filho, Victor H. Gonzalez Martinez, Juan Ricardo Muñoz
Results of stabilization for the higher order of the Kadomtsev-Petviashvili equation are presented in this manuscript. Precisely, we prove with two different approaches that under…
Two stability results for the Kawahara equation with a time-delayed boundary control
Roberto de A. Capistrano-Filho, Boumediène Chentouf, Luan S. de Sousa +1
In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this s…
Massera's theorems for a higher order dispersive system
Roberto de A. Capistrano-Filho, Isadora Maria de Jesus
This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties o…
Stabilization results for delayed fifth order KdV-type equation in a bounded domain
Roberto de A. Capistrano-Filho, Victor H. Gonzalez Martinez
Studied here is the Kawahara equation, a fifth order Korteweg-de Vries type equation, with time-delayed internal feedback. Under suitable assumptions on the time delay coefficients…
On the control issues for higher-order nonlinear dispersive equations on the circle
Roberto de A. Capistrano-Filho, Chulkwang Kwak, Francisco J. Vielma Leal
The local and global control results for a general higher-order KdV-type operator posed on the unit circle are presented. Using spectral analysis, we are able to prove local result…
Controllability for Schrödinger type system with mixed dispersion on compact star graphs
Roberto de A. Capistrano-Filho, Márcio Cavalcante, Fernando Gallego
In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger equation. Precisely, we are able to p…
Rapid Exponential Stabilization of a Boussinesq System of KdV--KdV Type
Roberto de A. Capistrano Filho, Eduardo Cerpa, Fernando A. Gallego
This paper studies the exponential stabilization of a Boussinesq system describing the two-way propagation of small amplitude gravity waves on the surface of an ideal fluid, the so…
Control results for a model of resonant interaction between short and long capillary-gravity waves
Roberto de A. Capistrano-Filho, Ademir Pampu
The purpose of this article is the investigation of the global control properties of a coupled nonlinear dispersive system posed in the periodic domain , a system with…
Global control aspects for long waves in nonlinear dispersive media
Roberto de A. Capistrano-Filho, Andressa Gomes
A class of models of long waves in dispersive media with coupled quadratic nonlinearities on a periodic domain are studied. We used two distributed controls, supported…
Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion
Roberto de A. Capistrano Filho, Thiago Yukio Tanaka
The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schrödinger equation with cubic nonlinearity. To obta…
Weak damping for the Korteweg-de Vries equation
Roberto de A. Capistrano-Filho
For more than 20 years, the Korteweg-de Vries equation has been intensively explored from the mathematical point of view. Regarding control theory, when adding an internal force te…
The fractional Schrödinger equation on compact manifolds: Global controllability results
Roberto de A. Capistrano Filho, Ademir Pampu
The goal of this work is to prove global controllability and stabilization properties for the fractional Schrödinger equation on -dimensional compact Riemannian manifolds withou…
Pointwise control of the linearized Gear-Grimshaw system
Roberto A. Capistrano-Filho, Vilmos Komornik, Ademir F. Pazoto
In this paper we consider the problem of controlling pointwise, by means of a time dependent Dirac measure supported by a given point, a coupled system of two Korteweg-de Vries equ…