Since 2000, I have been the director of studies and in 2006 I was appointed head of the mathematics unit at ITN. I received my PhD in 1995 under the supervision of Professor V. G. Maz'ya at the Department of Mathematics (MAI) at LiU in the field of Ill-posed and Inverse Problems. During my time at LiU, I have been the main supervisor for two doctoral students and co-supervisor for two more. I have been both the main applicant and co-applicant for grants for 15 different research projects.
George Baravdish
Senior Associate Professor, Head of Unit
Presentation
Senior associate professor of applied mathematics at the Unit of Physics, Electronics and Mathematics (FEM) at the Department of Science and Technology (ITN), Linköping University.
Publications
2024
A Hybrid Sobolev Gradient Method for Learning NODEs
Operations Research Forum, Vol. 5, Article 91
(Article in journal)
https://dx.doi.org/10.1007/s43069-024-00377-x
Brain Tumour Evolution Backwards in Time via Reaction-Diffusion Models and Sobolev Regularisation
Modelling and Computational Approaches for Multi-scale Phenomena in Cancer Research: From Cancer Evolution to Cancer Treatment
(Chapter in book)
https://dx.doi.org/10.1142/q0424
On a new singular and degenerate extension of the p-Laplace operator
Nonlinear Analysis, Vol. 244, Article 113553
(Article in journal)
https://dx.doi.org/10.1016/j.na.2024.113553
2023
Identifying a response parameter in a model of brain tumour evolution under therapy
IMA Journal of Applied Mathematics, Vol. 88, p. 378-404
(Article in journal)
https://dx.doi.org/10.1093/imamat/hxad013
2020
Generalizations of p-Laplace operator for image enhancement: Part 2
Communications on Pure and Applied Analysis, Vol. 19, p. 3477-3500
(Article in journal)
https://dx.doi.org/10.3934/cpaa.2020152
My research
My research deals with ill-posed and inverse problems that took off at the turn of the century when well-posed problems were defined, i.e. problems that have a unique solution and depend continuously on the input data. This means that ill-posed problems are difficult to solve because even though they describe physical situations with a unique solution, they are numerically unstable. Many inverse problems are also ill-posed. Inverse problems are when the output is given but the model or input is unknown. As computers have become more powerful in recent decades, research on these problems has also taken off. Ill-posed and inverse problems in mathematics can be found in complex analysis, functional analysis, differential equations, and linear algebra.
In application areas, they can be found in machine learning, signal processing, computer vision, control engineering, meteorology, geophysics, optics, and nuclear physics. Some of the classic questions that have been studied intensively are to reconstruct an initial temperature for a heat conduction equation given the temperature at a later time. Another well-known problem is the analytic continuation of harmonic solutions, i.e. solving the Cauchy problem for the Laplace equation.
Ongoing projects
Right now I am working on these projects and have various collaborations:
Additional research
In addition to the projects that can be read more about via the links above, my research has the following focus:
Image processing
I have collaborated with several different researchers for a long time to study mathematical models in image processing and computer vision where we have proposed (a) Various optimization models for image enhancement (b) Generalization of the p-Laplace operator for noise reduction.
Telecommunications
Here I have studied the problem of reconstructing 3D objects using Wi-Fi signals, AI, and Compressed Sensing.
Inverse and Ill-Posed Problems: Theory and Algorithms
This project constitutes the mathematical core of my research areas that I have continued to develop and generalize both theory and methods applied to ODE and PDE, which are the mathematical models in the research areas listed above.