17 citations · 44 across the 14 of their papers we have counts for
14 papers
Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition
Alexander Rodriguez, Eduardo Cerpa
In this paper we study the FitzHugh-Nagumo system posed on the half-line with a sinusoidal forcing term acting at the origin through the Neumann boun\-da\-ry condition. By applying…
The impact of high frequency-based stability on the onset of action potentials in neuron models
Eduardo Cerpa, Nathaly Corrales, Matías Courdurier +2
This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onse…
Stability analysis of a linear system coupling wave and heat equations with different time scales
Gonzalo Arias, Eduardo Cerpa, Swann Marx
In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a fact…
Approximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources
Eduardo Cerpa, Matías Courdurier, Esteban Hernández +2
The use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Nonlinear differential equat…
Singular perturbation analysis for a coupled KdV-ODE system
Swann Marx, Eduardo Cerpa
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when diffe…
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…
Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions
Eduardo Cerpa, Cristhian Montoya, Bingyu Zhang
This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary condition…
Output feedback stabilization of the Korteweg-de Vries equation *
Swann Marx, Eduardo Cerpa
This paper presents an output feedback control law for the Korteweg-de Vries equation. The control design is based on the backstepping method and the introduction of an appropriate…
Global stabilization of a Korteweg-de Vries equation with saturating distributed control
Swann Marx, Eduardo Cerpa, Christophe Prieur +1
This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathemat…
Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L 2 -norm
Swann Marx, Eduardo Cerpa, Christophe Prieur +1
This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a Korteweg-de Vries equation, which is a nonlinear mathe…
Stabilization of a linear Korteweg-de Vries equation with a saturated internal control
Swann Marx, Eduardo Cerpa, Christophe Prieur +1
This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathemat…
Output feedback control of the linear Korteweg-de Vries equation
Swann Marx, Eduardo Cerpa
- This paper presents the design of an output feedback control for a linear Korteweg-de Vries equation. This design is based on the backstepping method which uses a Volterra transf…
Boundary Controllability of the Korteweg-de Vries Equation on a Bounded Domain
Eduardo Cerpa, Ivonne Rivas, Bing-Yu Zhang
This paper is devoted to study boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation…
Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation
Lucie Baudouin, Eduardo Cerpa, Emmanuelle Crépeau +1
This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diff…