Assistant Doctor (Teaching and Research staff)
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| My research interest is Control Theory and Inverse Problems for Partial Differential Equations (PDE) and Fractional Differential Equations (FDE). | |||||
| ORCID | WoS: AAY-2547-2020 | Scopus: 16644226500 | |||||
I am an Assistant Doctor (Teaching and Research staff) at the University of Deusto, Basque Country, Spain. I have a PhD in Engineering Sciences, mention in Mathematical Modeling from the University of Chile and I am a Mathematical Engineer from the University of Santiago of Chile, where I was recently an Associate Professor between 2019 and 2024. During the academic year 2023-2024 I did a one-year research stay at the Friedrich-Alexander-University, Erlangen, Germany, under the Research Fellowship for Experienced Researchers of the Alexander von Humboldt Foundation.
My research interest is Control Theory and Inverse Problems for Partial Differential Equations (PDE) and Fractional Differential Equations (FDE). Specifically, my fields of research are: inverse problems for water waves, nonlocal equations, and fluid mechanics models; optimal control problems and turnpike phenomenon for PDEs and FDEs; stabilization of PDEs and FDEs; controllability of PDEs and FDEs.
- PhD in Engineering Sciences, Mention in Mathematical Modeling (2016) University of Chile, Chile
- Mathematical Engineering Degree (2011). University of Santiago of Chile, Chile
- Bachelor in Mathematics (2010). University of Santiago of Chile, Chile
PhD Thesis: Inverse problems and controllability in fluid mechanics models
Advisor: Jaime Ortega / Co-advisor: Rodrigo Lecarós
This thesis is devoted to the study of inverse and control problems in the area of fluid mechanics. We focus on Stokes and Navier–Stokes equations, both stationary and evolutionary systems which are well known to the mathematical development of incompressible viscous flows. View PhD Thesis
Released
Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
Boundary Controllability for the 1D Moore-Gibson-Thompson equation
Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields
Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions
An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound
Submitted
Averaged observations and turnpike phenomenon for parameter-dependent systems
Almost periodic turnpike phenomenon for time-dependent systems
Tracking controllability for finite-dimensional linear systems
- 2023 - 2024. Humboldt Research Fellowship for Experienced Researchers. Alexander von Humboldt Foundation. Principal investigator, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany.
- 2019 - 2022. Principal investigator, Faculty of Science, Mathematics and Computer Science Department, University of Santiago of Chile, Chile. ANID-PAI Convocatoria Nacional Subvención a la Instalación en la Academia a ̃no 2019 Grant No. PAI77190106
- 2018 - 2021. Principal investigator, Faculty of Science, Mathematics and Computer Science Department, University of Santiago of Chile, Chile. Postdoctoral FONDECYT Grant No. 3180322
- 2017. Postdoctoral fellow, Faculty of Science, Mathematics and Computer Science Department, University of Santiago of Chile, Chile. Dicyt-USACH Grant No. 041633LY-POSTDOC
- 2012 - 2016. PhD fellow, Mathematical Engineering Department, University of Chile, Chile PhD scholarship CONICYT-Nacional 2012. No. 21120662
- 08.2022. IX Partial Differential Equations, Optimal Design and Numerics, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain
- 07.2022. CEDYA 2022. Congreso de Ecuaciones Diferenciales y Aplicaciones, Universidad de Zaragoza, Zaragoza, Spain
- 09.2021. CLAM 2021. Congreso Latinoamericano de Matemáticos, Universidad de la República del Uruguay, Montevideo, Uruguay
- 08.2021. IFIP TC7. Conference on System Modelling and Optimization, Escuela Politécnica Nacional, Quito, Ecuador
- 04.2021. XXXIII Jornada de Matemática de la Zona Sur, Universidad de la Frontera, Temuco, Chile
- 11.2019. Null controllability from the exterior of a one-dimensional nonlocal heat equation. French Latin–American Conference on New Trends in Applied Mathematics - FLACAM 2019, University of Chile, Santiago, Chile.
- 09.2019. Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustic. European Numerical Mathematics and Advanced Applications Conference 2019 - ENUMATH 2019, Egmond aan Zee, Holland.
- 08.2019. Exterior control problem of strong damped nonlocal wave equation and nonlocal heat equation. VII Partial Differential Equations, Optimal Design and Numerics, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain
- 08.2019. Turnpike property for 2 and 3–D Navier–Stokes systems. VII Partial Differential Equations, Optimal Design and Numerics, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain
- 06.2019. Analysis of the controllability from the exterior of strong damping nonlocal wave equation. Coloquio IMAFI, Instituto de Matemática y Física, Universidad de Talca, Talca, Chile
- 12.2018. Analysis of the controllability from the exterior of strong damping nonlocal wave equation. Workshop on Inverse and Control Problems for Physical Systems, Universidad Técnica Federico Santa María, Valparaíso, Chile
- 11.2018. Controllability of PDE: moving control. III Workshop de Ciencia, University of Santiago of Chile, Santiago, Chile
Teaching Experience at University of Deusto
Undergraduate Courses in Mathematical Engineering
- Fundamentals of Algebra (2024/1) Probability (2024/2)
Undergraduate Courses in Engineering and Sciences
- Differential Equations (2024/1) Calculus I (2024/2)
Teaching Experience at University of Santiago of Chile
Undergraduate Courses in Mathematical Engineering
- Algebra I (2018/1, 2019/1, 2020/1, 2022/1, 2023/1)
- Calculus I (2017/2)
- Introduction to Engineering (2017/2, 2018/2, 2020/2, 2022/2) Topology (2021/1)
- Functional Analysis (2021/1)
- Complex Analysis (2016/2)
- Probabilities (2013/2, 2016/2)
- Seminar on Control of Partial Differential Equations (2018/2, 2020/2, 2022/2)
- Seminar on Analysis and Applications of the Navier-Stokes equations (2016/2)
- Seminar on Controllability and Optimal Control (2014/2)
- Seminar on Sobolev spaces and applications (2013/2)
Undergraduate Courses in Engineering and Sciences
- Differential Equations and Numerical Methods (2021/1, 2022/1, 2023/1)
- Algebra I (2017/2)
- Calculus I (2010/1, 2011/1, 2012/1, 2013/1)
- Calculus II (2010/2, 2011/2, 2012/2, 2013/2)
Graduate Courses in Master in Mathematics
- Topology (2021/1)
- Seminar on Control of Partial Differential Equations (2018/2)
- Seminar on Sobolev spaces and applications (2013/2)
Teaching Experience at University of Chile
Undergraduate Courses in University of Chile
- Differential and Integral Calculus (2016/2, 2017/1, 2017/2)
- Ordinary differential equations (2017/2)
- Probabilities and Statistics (2014/2, 2016/2)
- Mathematics III (2017/2, 2018/2)
Teaching Experience at Adolfo Ibáñez University
- Linear Algebra (2016/2)
- Ordinary differential equations (2016/2)
- Calculus II (2016/1)
- Probability Theory (2014/2)
- Applied Statistics (2014/2)
- Analytical Geometry and Introduction to Calculus (2014/1)