Visiting Professor

My research interests include Inverse Problems, Partial Differential Equations, Control Theory, Optimization, Numerical Analysis, Mathematical Modeling, Calculus of Variations, Controllability, Stability, Water Waves, Fluid Mechanics, Numerical Methods for PDEs, Shock Waves, Discrete Systems, Stochastic Partial Differential Equations

Areas of Interest: My areas of interest are centered on Inverse Problems, Partial Differential Equations, Control Theory, Optimization, and Numerical Analysis. I also dedicate myself to Mathematical Modeling, the Calculus of Variations, Controllability and Stability of systems, as well as the study of Water Waves, Fluid Mechanics, Numerical Methods for PDEs, Shock Waves, Discrete Systems, and Stochastic Partial Differential Equations.

Professional Experience: I have an extensive background as a Civil Engineer in Mathematics and a Ph.D. in Engineering Sciences with a mention in Mathematical Modeling, currently serving as an Associate Professor at Universidad Técnica Federico Santa María. My experience combines academia with industry, having worked as a Scientist at the Center for Mathematical Modeling (CMM) at Universidad de Chile, where I participated in relevant projects on seismic risk assessment (including the development of GEOSIS software) and in the creation of geographic information systems for slope stability analysis. My previous roles as a Project Engineer included implementing numerical models for contaminant transport in mining, developing economic models for water pricing, and working on fiber optic network installations for deformation estimation in underground mining. Additionally, I completed a postdoctoral fellowship at the Basque Center for Applied Mathematics (BCAM) in Spain, focusing on numerical methods for optimal control problems. Throughout my career, I have been involved in diverse projects, including analysis for CODELCO, maintaining a strong focus on applying mathematical modeling to solve industrial problems, especially in the mining sector.  

PhD in Engineering Sciences, mention in Mathematical Modeling (2012) University of Chile
Bachelor of Science in Engineering, mention in Mathematics (2003) Universidad de Chile, Chile

• Book Chapter: Lecaros, R., Zuazua, E. (2014). Tracking Control of 1D Scalar Conservation Laws in the Presence of Shocks. In: Trends in Contemporary Mathematics. Springer International Publishing.
• Lecaros, R., Lopez-Rios, J., Perez, AA. (2025). Lipschitz stability in inverse problems for semi-discrete parabolic operators. arXiv preprint arXiv:2504.01143.
• Lecaros, R., Perez, AA., Prado, MF. (2025). Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability. arXiv preprint arXiv:2503.03596.
• Lecaros, R., Lopez-Rios, J., Montecinos, GI., Zuazua, E. (2024). Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements. Mathematical Methods in the Applied Sciences, 47(18), 13973-14004.
• Fontelos, MA., Lecaros, R., Lopez-Rios, J., Perez, A. (2024). Controllability for a non-local formulation of surface gravity waves. arXiv preprint arXiv:2402.18468.
• Lecaros, R., Morales, R., Perez, A., Zamorano, S. (2023). Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions. Journal of Differential Equations, 365, 832-881.
• Hernandez, M., Lecaros, R., Zamorano, S. (2023). Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields. (Note: Journal details like volume/page might be needed here if it’s not a preprint).
• Lecaros, R., Ortega, JH., Perez, A., De Teresa, L. (2023). Discrete Calder ́on problem with partial data. Inverse Problems, 39(3), 035001.
• Arancibia, R., Lecaros, R., Mercado, A., Zamorano, S. (2022). An Inverse Problem For Moore-Gibson-Thompson Equation arising in High Intensity Ultrasound. J. of Inverse and Ill-posed problems.
• Cerpa, E., Lecaros, R., Neguyen, T. N. T., P ́erez, A. (2022). Carleman estimates and controllability for a semi-discrete fourth-order parabolic equation. J. de Math ́ematiques Pures et Appliquées.

  • 04.07.2025. DeustoCCM seminar: Lipschitz stability in inverse problems for semi-discrete parabolic operators
Meet our team!