Borjan Geshkovski is a PhD Student at Universidad Autónoma de Madrid (UAM). He earned a MSc in Mathematics at the University of Bordeaux, during which he did an internship on the topic “Obstacle problems: theory and Applications” within the DyCon team.
Currently, he is studying for a PhD in Control Theory under the supervision of Professor Enrique Zuazua.
“My research interests are focused on the control-theoretical aspects (controllability, stabilization, optimization) of free boundary problems arising in fluid mechanics, thermodynamics and elasticity.”
- MSc in Applied Mathematics (2016 – 2018), Université de Bordeaux, France.
- BSc in Applied Mathematics and Computer Science (2012 – 2016), Université de Bordeaux, France.
- 23.08.2019 Control of perturbed porous medium flow , 8th Workshop on PDE, Optimal Design and Numerics, Centro de Ciencias “Pedro Pascual”, Benasque, Spain. Slides
- 06.05.2019 Control of linearized porous medium flow, Workshop on homogenization, spectral theory and other topics in PDEs, ICMAT Madrid, Spain. Slides
- 20.02.2019 Control of free boundary problems, Second Network meeting of the ConFlex consortium, Bilbao, Spain. Slides
- 20.01.2019 Control and free boundaries, Friedrich-Alexander Universität, Erlangen, Germany. Slides
- 27.04.2018 Obstacle problems, optimal control and numerics, DeustoTech, Bilbao, Spain. Slides
Obstacle Problems: Theory and Applications
Advisor: Prof. Enrique Zuazua
Abstract: In this master thesis, we present a study of the analytical and optimal control properties for the elliptic and parabolic obstacle problems. The obstacle problem is one of the simplest and most physically relevant free boundary problems. From a mathematical perspective, similar questions as for classical partial differential equations (well-posedness, regularity, optimal control) are addressed, as well as the conception of appropriate numerical schemes and computer simulations of the these problems. This work was supported by the Advanced Grant DyCon (Dynamic Control) of the European Research Council Executive Agency (ERC).
Document: PDF file of the thesis can be found here.
- Awarded the “Best Review and Presentation Prize” at the second ConFlex workshop held in Bilbao, from February 11 to 21, 2019
- Analysis, numerics and control for the obstacle problem
- LQR optimal control design for a coupled PDE-ODE system