30 citations · 79 across the 17 of their papers we have counts for
18 papers
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 Effects on the Controllability of Coupled KdV Systems
F. A. Gallego, A. F. Pazoto, I. Rivas
We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weak…
Biorthogonal functions for complex exponentials and an application to the controllability of the Kawahara equation via a moment approach
Ademir F. Pazoto, Miguel Soto
The paper deals with the controllability properties of the Kawahara equation posed on a periodic domain. We show that the equation is exactly controllable by means of a control dep…
Unique continuation and time decay for a higher-order water wave model
Ademir F. Pazoto, Miguel Soto
This work is devoted to prove the exponential decay for the energy of solutions of a higher order Korteweg -de Vries (KdV)--Benjamin-Bona-Mahony (BBM) equation on a periodic domain…
A Convection-Diffusion model on a star shaped graph
Cristian M. Cazacu, Liviu I. Ignat, Ademir F. Pazoto +1
In this paper we study a convection-diffusion equation on a star-shaped graph composed by incoming edges and outgoing edges with a nonlinearity $f\in C^1(\rr)$ satisfying s…
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…
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…
Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped trees
Cristian M. Cazacu, Liviu I. Ignat, Ademir F. Pazoto
In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is c…
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…
On the well-posedness and asymptotic behavior of the generalized KdV-Burgers equation
Fernando Andrés Gallego, Ademir Fernando Pazoto
In this paper we are concerned with the well-posedness and the exponential stabilization of the generalized Korteweg-de Vries Burgers equation, posed on the whole real line, under…
On The Asymptotic Behavior Of A Subcritical Convection-Diffusion Equation With Nonlocal Diffusion
C. Cazacu, L. Ignat, A. Pazoto
In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estima…
Internal controllability of the Korteweg-de Vries equation on a bounded domain
Roberto Capistrano Filho, Ademir Pazoto, Lionel Rosier
This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an ar…
Large time behaviour for a nonlocal diffusion - convection equation related with the gas dynamics
Liviu I. Ignat, Ademir Pazoto
In this paper we consider a model that involves nonlocal diffusion and a classical convective term. Using a scaling argument and a new compactness argument we obtain the first term…
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…
Well-posedness and stabilization of a model system for long waves posed on a quarter plane
Ademir Fernando Pazoto, Gilmar dos Reis Souza
In this paper we are concerned with a initial boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized dam…
Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line
Ademir Pazoto, Lionel Rosier
Studied here is the large-time behavior of solutions of the Korteweg-de Vries equation posed on the right half-line under the effect of a localized damping. Assuming as in \cite{li…