Abubakar Mwasa defended his doctoral thesis successfully at the Department of Mathematics at Linköping University on the 25 Mars. In the thesis ”Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form” Mwasa looks at different aspects of solutions to partial differential equations, or PDEs.
Abubakar Mwasa nailing his thesis.– Many problems in Sciences are modelled by partial differential equations (PDEs). For instance in physics, to minimise energy of some physical quantity through a medium, a certain PDE is used. The solutions to these equations describe the density of the physical quantity in equilibrium e.g. the electrostatic potential or the temperature distribution in a body. Most solutions to such equations are not smooth enough to be solutions in the classical sense, but rather are understood in some generalised way as weak solutions by means of the so-called Sobolev spaces. With these spaces, one strives to answer the following questions. Existence: Do these solutions exist and if so, under what standard conditions? Uniqueness: Are they the only solutions? And possibly one may ask how do such solutions behave in certain regions? In this thesis, we explore some of these aspects about the generalised solutions for some type of PDEs (Nonlinear elliptic equations) in both bounded and unbounded regions, says Abubakar Mwasa.
In what areas can your research contribute?
– The results contribute to the general understanding of the behaviour of generalised solutions of PDEs in a given medium. These can be applied in electromagnetism, electrostatics, fluid dynamics and image analysis.
Has the current pandemic affected your work in any way?
– Well, this is two fold: First, it was not possible to visit my family for the whole year and also restricted social interactions. The planned research dissemination activities like seminars and conferences were cancelled. On the other hand, the extended stay without holiday from autumn 2019 to autumn 2020 enabled me to complete many research tasks.
How was the public disputation?
Abubakar Mwasa with the opponent Sorina Barza and supervisors Thomas Sjödin, Anders Björn and Jana Björn.– I would say it was very successful. I had fruitful discussions with the opponent and the examination committee. It was a milestone event in my life. There was a wide audience because of the digital setup which my wife and colleagues from Uganda attended. Even though, it was not possible to have usual social events after the defence like cake.
What is next for you?
– I will continue doing research in mathematical analysis, community outreach and teaching at my home university, Busitema University, Uganda. I will definitely go back to Uganda and apply not only the knowledge accumulated while at Linköping University but also the great norms learnt from Sweden.