arXiv subjects

George J. Bautista

Publications and source records attributed to George J. Bautista.

4 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

Studies on the Rao-Nakra Sandwich Beam: Well-Posedness, Dynamics, and Controllability

In this work, we investigate the well-posedness, stabilization, and boundary controllability of a linear Rao-Nakra type sandwich beam. The system consists of three coupled equations that represent the longitudinal displacements of the outer layers and the transverse displacement of the composite beam, all of which are coupled with dynamical boundary conditions. In the first problem, time-varying interior damping and static boundary conditions with time-dependent delays are considered. Then, we establish the existence and uniqueness of solutions for the Cauchy problem associated with the damped system using semigroup theory and a classical result by Kato. Furthermore, employing a Lyapunov-based approach, we prove that the system's energy decays exponentially, despite the presence of time-varying weights and delays. In the second problem, we consider a boundary linear control system with dynamical boundary conditions, and prove its well-posedness. By deriving an observability inequality for the adjoint system and applying the Hilbert Uniqueness Method (HUM), we show that the system is null controllable. A key contribution of this work lies in handling the full three-equation coupled system, which involves significant difficulty due to the dynamic boundary conditions, resolved via appropriately constructed Lyapunov functionals and intermediate observability inequalities.

math.OC↗

arXiv2025

On the controllability of laminated beams with Venttsel-type boundary conditions

This paper examines the boundary controllability of a Timoshenko laminated beam system subject to Venttsel-type boundary conditions. The study focuses on a novel configuration in which three controls are applied solely at the boundary of the beam. Controllability is established by deriving an appropriate observability inequality for the corresponding adjoint system, which is then employed within the framework of the duality method in the setup of the classical Hilbert uniqueness method (HUM) to achieve the control problem. The main contribution lies in the analysis of a system comprising three beams governed by dynamic Venttsel-type boundary conditions, as introduced by Venttsel in [Theory Probab. Appl., 4 (1959)].

math.OC↗

arXiv2024

Numerical approximation of the insitu combustion model using the nonlinear mixed complementarity method

In this work, we will study a numerical method that allows finding an approximation of the exact solution for a in-situ combustion model using the nonlinear mixed complementary method, which is a variation of the Newtons method for solving nonlinear systems based on an implicit finite difference scheme and a nonlinear algorithm mixed complementarity, FDA-MNCP. The method has the advantage of provide a global convergence in relation to the finite difference method and method of Newton that only has local convergence. The theory is applied to model in-situ combustion, which can be rewritten in the form of mixed complementarity also we do a comparison with the FDA-NCP method

math.NA↗