arXiv subjects

Alfredo S. Gamboa

Publications and source records attributed to Alfredo S. Gamboa.

5 recordsLinked to original sources

arXiv2026

Decay of solutions and bilinear control to trajectories of a 1D degenerate parabolic system

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 parabolic systems with weakly degenerate diffusion coefficients. The system is controlled through the coefficient of the reaction term. Our approach relies on a well-known local inversion method combined with suitable a priori estimates specifically adapted to the degenerate setting.

math.AP↗

arXiv2026

Bilinear control to trajectories of 1D degenerate parabolic equations in moving domains

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 exact controllability to a positive trajectory of a one-dimensional semilinear degenerate equation governed via the coefficient of the reaction term. We apply a well-known local inversion method combined with some appropriate specific estimates.

math.AP↗

arXiv2026

Nash-Stackelberg controllability for coupled systems of degenerate equations in non-cylindrical domains

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 controllability of the semilinear system using Liusternik's inverse function theorem. Nevertheless, the main difficulty is to adapt a Carleman estimate for the controllability of the linearized otimality system, using a Carleman inequality for degenerate non-autonomous equation obtanied by the authors previously.

math.AP↗

arXiv2025

Stackelberg-Nash strategy for the null controllability of semilinear degenerate equations in non-cylindrical domains

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 where the diffusion coefficient degenerates at one point of the boundary. The linearized degenerated system is treated using a Carleman inequality for degenerated non-autonomous systems proved by the autors in [19] and the local controllability of the semilinear system is obtained using Liusterniks inverse function theorem.

math.AP↗

arXiv2025

Controllability of a system of non-autonomous degenerate coupled parabolic equations

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 diffusion term. Then we use the estimate to show the null controllability of a coupled system characterized by this form of diffusion operator and bounded coefficients.

math.AP↗