Patricio Guzmán

I am an Assistant Professor at the Departamento de Matemática of the Universidad Técnica Federico Santa María, which is where I got the professional title of Mathematical Engineer and later the academic degrees of M.Sci and Ph.D. in Mathematics. During my formal education I had the privilege to be directed by Eduardo Cerpa, Lionel Rosier and Alberto Mercado. My work as postdoctoral researcher at the Centro de Modelamiento Matemático of the Universidad de Chile was supervised by Axel Osses.

Research

I am interested in control theory. I am currently studying the controllability and stabilization of partial differential equations, with special interest to those coming from applied models. I participate in the following research projects.

MATH-AMSUD AMSUD220023 (National Coordinator). Stabilization, Control and Inverse Problems in PDEs.
FONDECYT 11240290 (Responsible). Rapid Stabilization of Partial Differential Equations with Disturbances.

Journal Papers

P. Guzmán and E. Hernández.

Rapid stabilization of an unstable heat equation with disturbance at the flux boundary condition.

Submitted. (2024).
[9]P. Guzmán and E. Hernández.

Stabilization of the heat equation with disturbance at the flux boundary condition.

Math. Methods. Appl. Sci. 46 (17) (2023) 18035-18043.
[8]P. Guzmán and L. Rosier.

Null controllability of the structurally damped wave equation on the two-dimensional torus.

SIAM J. Control Optim. 59 (1) (2021) 131-155.
[7]P. Guzmán.

Local exact controllability to the trajectories of the Cahn-Hilliard equation.

Appl. Math. Optim. 82 (1) (2020) 279-306.
[6]P. Guzmán.

Boundary stabilization of a microbeam model.

Math. Methods. Appl. Sci. 43 (9) (2020) 5979-5984.
[5]P. Guzmán.

Energy decay of a microbeam model with a locally distributed nonlinear feedback control.

J. Math. Anal. Appl. 467 (1) (2018) 238-252.
[4]E. Cerpa, P. Guzmán and A. Mercado.

On the control of the linear Kuramoto-Sivashinsky equation.

ESAIM Control Optim. Calc. Var. 23 (1) (2017) 165-194.
[3]N. Carreño and P. Guzmán.

On the cost of null controllability of a fourth-order parabolic equation.

J. Differential Equations 261 (11) (2016) 6485-6520.
[2]P. Guzmán and J. Zhu.

Exact boundary controllability of a microbeam model.

J. Math. Anal. Appl. 425 (2) (2015) 655-665.
[1]P. Guzmán.

Lipschitz stability in an inverse problem for the main coefficient of a Kuramoto-Sivashinsky type equation.

J. Math. Anal. Appl. 408 (1) (2013) 275–290.

Conference Papers

[2]P. Guzmán and C. Prieur.

Rapid stabilization of a reaction-diffusion equation with distributed disturbance.

59th IEEE Conference on Decision and Control; Jeju Island, Korea, 2020.
[1]P. Guzmán, S. Marx and E. Cerpa.

Stabilization of the linear Kuramoto-Sivashinsky equation with a delayed boundary control.

3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations.

and XI Workshop Control of Distributed Parameter Systems; Oaxaca, México, 2019.

Former Students

[3]Tomás Cortés (January 13, 2023) / Codirected with Rodrigo Lecaros.

On the null controllability of parabolic equations and applications.

Mathematical Engineering and M.Sci. in Mathematics.
[2]Gonzalo Arias (January 20, 2021) / Codirected with Eduardo Cerpa.

Stabilization of a microbeam model with distributed disturbance.

Mathematical Engineering and M.Sci. in Mathematics.
[1]Hugo Parada (September 1, 2020) / Codirected with Eduardo Cerpa.

Feedback stabilization of some unstable elliptic-parabolic systems.

Mathematical Engineering and M.Sci. in Mathematics.