10 papers · 1 filter
Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system
Cristian Loli, George J. Bautista, Juan Limaco +3
In this manuscript, we are concerned with the hierarchical control of a non-degenerate quasi-linear parabolic system, posed on a bounded interval. We use the Stackelberg-Nash strat…
Decay of solutions and bilinear control to trajectories of a 1D degenerate parabolic system
Alfredo S. Gamboa, André Da Rocha Lopes, Luis P. Yapu
This paper is concerned with the decay of solutions and the analysis of the local and global exact controllability to trajectories for a class of one-dimensional nonlinear paraboli…
Bilinear control to trajectories of 1D degenerate parabolic equations in moving domains
Alfredo S. Gamboa, André da Rocha Lopes, Luis P. Yapu
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exa…
Nash-Stackelberg controllability for coupled systems of degenerate equations in non-cylindrical domains
Alfredo S. Gamboa, Juan Limaco, Luis P. Yapu
In this paper we investigate the Hierarchical null controllability of a coupled degenerate semilinear parabolic equation in domains which are moving in time. We show the local null…
Existence, Stability and Controllability of the parabolic-parabolic thermistor model
Miguel R. Nuñez-Chávez, Luis P. Yapu, Juan Límaco
In this article we establish the well-posedness, energy estimates, stability, and local null controllability for the thermistor system modeled by a parabolic-parabolic system using…
Controllability of a Semilinear System of Parabolic Equations with Nonlocal Terms
Juan Limaco, Rafael Martins Lobosco, Luis P. Yapu
This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as gen…
Local controllability of free boundary three-dimensional semilinear radial parabolic equations
Juan Límaco, Luis P. Yapu
We prove that a free boundary semilinear heat equation with Stefan boundary condition and radially symmetric data is locally null controllable. The strategy involves reducing the p…
Stackelberg-Nash strategy for the null controllability of semilinear degenerate equations in non-cylindrical domains
Alfredo S. Gamboa, Juan Limaco, Luis P. Yapu
In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain wher…
Controllability of a system of non-autonomous degenerate coupled parabolic equations
Alfredo S. Gamboa, Juan Limaco, Luis P. Yapu
We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the…
Scattering for the generalized Hartree equation with a potential
Carlos M. Guzmán, Cristian Loli, Luis P. Yapu
We consider the focusing generalized Hartree equation in with a potential, \begin{equation*} iu_t + Δu - V(x)u + (I_γ\ast |u|^p )|u|^{p-2} u=0, \end{equation*} where $I…