arXiv subjects

Juan Limaco

Publications and source records attributed to Juan Limaco.

5 recordsLinked to original sources

arXiv2026

Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system

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 strategy with a single control called leader and two controls called followers. First, we study the controllability for the linear system, where we will demonstrate a Carleman inequality associated with the adjoint problem. Then, using the results obtained for the linear case and applying Liusternik's Inverse Function Theorem, we obtain local null controllability for the quasi-linear problem.

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

Controllability of a Semilinear System of Parabolic Equations with Nonlocal Terms

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 generalized Black--Scholes models. We establish local null controllability at a fixed time T>0 for a class of semilinear, nonlocally coupled systems driven by a single internal control acting on one component. The proof combines Kakutani's fixed-point theorem with a controllability/observability estimate for the associated linearized dynamics. In addition, we obtain controllability for a broader class of linear systems than those considered in the first article. The paper concludes with remarks on boundary controllability within the same nonlocal framework and with perspectives for future research.

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.

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