24 citations · 159 across the 16 of their papers we have counts for
15 papers · 1 filter
Traveling-wave solutions for a higher-order Boussinesq system: existence and numerical analysis
Roberto de A. Capistrano-Filho, Juan Carlos Muñoz, José R. Quintero
We study the existence and numerical computation of traveling wave solutions for a family of nonlinear higher-order Boussinesq evolution systems with a Hamiltonian structure. This…
Another look at the control properties of the Korteweg-de Vries equation
Roberto de A. Capistrano-Filho, Fernando Gallego
This paper represents a new perspective in understanding the controllability of the Korteweg-de Vries (KdV) equation on unbounded domains. By studying the equation on both the righ…
Well-posedness and controllability of Kawahara equation in weighted Sobolev spaces
Roberto de A. Capistrano Filho, Milena de S. Gomes
We consider the Kawahara equation, a fifth order Korteweg-de Vries type equation, posed on a bounded interval. The first result of the article is related to the well-posedness in w…
Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
Roberto A. Capistrano-Filho, Márcio Cavalcante, Fernando A. Gallego
This paper deals with the initial-boundary value problem of the biharmonic cubic nonlinear Schrödinger equation in a quarter plane with inhomogeneous Dirichlet-Neumann boundary dat…
Initial boundary value problem for Korteweg-de Vries equation: a review and open problems
Roberto de A. Capistrano-Filho, Shu-Ming Sun, Bing-Yu Zhang
In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note…
Stabilization and control for the biharmonic Schrödinger equation
Roberto Capistrano Filho, Márcio Cavalcante
The main purpose of this paper is to show the global stabilization and exact controllability properties for a fourth order nonlinear fourth order nonlinear Schrödinger system: $$i\…
On the well posedness and large-time behavior of higher order Boussinesq system
R. A. Capistrano-Filho, F. A. Gallego, A. F. Pazoto
A family of Boussinesq systems has been proposed to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investi…
Control of a Boussinesq system of KdV-KdV type on a bounded interval
Roberto A. Capistrano-Filho, Ademir F. Pazoto, Lionel Rosier
We consider a Boussinesq system of KdV-KdV type introduced by J. Bona, M. Chen and J.-C. Saut as a model for the motion of small amplitude long waves on the surface of an ideal flu…
Asymptotic behavior of Boussinesq system of KdV-KdV type
Roberto A. Capistrano-Filho, Fernando A. Gallego
This work deals with the local rapid exponential stabilization for a Boussinesq system of KdV-KdV type introduced by J. Bona, M. Chen and J.-C. Saut. This is a model for the motion…
General Boundary Value Problems of the Korteweg-de Vries Equation on a Bounded Domain
R. A. Capistrano-Filho, Shu-Ming Sun, Bing-Yu Zhang
In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval \begin{equation} u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=ϕ(x)…
Stabilization of the Gear-Grimshaw system with weak damping
R. A. Capistrano-Filho
The aim of this work is to consider the internal stabilization of a nonlinear coupled system of two Korteweg--de Vries equations in a finite interval under the effect of a very wea…
Boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations with critical size restrictions on the spatial domain
Roberto A. Capistrano-Filho, Fernando A. Gallego, Ademir F. Pazoto
This article is dedicated to improve the controllability results obtained by Cerpa et al. in Commun. Contemp. Math 13 (2011) and by Micu et al. in Commun. Contemp. Math 11 (5) (200…
Neumann Boundary Controllability of the Gear--Grimshaw System With Critical Size Restrictions on the Spacial Domain
Roberto de A. Capistrano-Filho, Fernando A. Gallego, Ademir F. Pazoto
In this paper we study the boundary controllability of the Gear-Grimshaw system posed on a finite domain , with Neumann boundary conditions: \begin{equation} \label{abs} \be…
Neumann boundary controllability of the Korteweg-de Vries equation on a bounded domain
Miguel Caicedo, Roberto de A. Capistrano-Filho, Bingyu Zhang
In this paper we study boundary controllability of the Korteweg-de Vries (KdV) equation posed on a finite domain with the Neumann boundary conditions: u_t+u_x+uu_x+u_{xxx}=…
Stabilization of the Gear-Grimshaw system on a periodic domain
Roberto A. Capistrano-Filho, Vilmos Komornik, Ademir F. Pazoto
This paper is devoted to the study of a nonlinear coupled system of two Korteweg-de Vries equations in a periodic domain under the effect of an internal damping term. The system wa…