My area of specialisation is mathematical analysis, evolutionary partial differential equations, and the development and implementation of numerical algorithms. My research concerns both direct and inverse problems in heat transfer, fractional calculus, elasticity, electromagnetism, and thermoelasticity.
The mathematical analysis of these problems, including existence and uniqueness of solutions, is mainly based on variational methods combined with time-discretisation techniques. I am also interested in convergence and error analysis, as well as the stability and robustness of numerical algorithms.
My doctoral supervision has focused on the mathematical analysis and numerical approximation of partial differential equations arising in heat transfer, thermoelasticity, and electromagnetism. The following PhD theses were completed at Ghent University.
Thesis: Direct and inverse problems for partial differential equations in models of heat and thermoelasticity (Doctor of Science: Mathematics, 2025).
This research investigated direct and inverse problems for fractional heat equations and coupled thermoelastic systems, including models with time delays. The direct problems involved establishing the existence and uniqueness of weak solutions. The inverse problems focused on identifying unknown, space-dependent source terms from measurements. Numerical reconstruction methods and regularisation techniques were also studied.
Supervisors: Karel Van Bockstal, Marian Slodička, and Denis Constales.
Thesis: Advanced mathematical and numerical analysis of induction hardening of steel (Doctor of Science: Mathematics, 2022).
This research concerned the mathematical modelling and numerical analysis of induction hardening, an industrial process in which electromagnetic fields heat a steel workpiece. The work addressed coupled nonlinear partial differential equations describing electromagnetic and thermal effects, including mathematical well-posedness and numerical discretisation. Particular attention was given to the analysis of models incorporating phase transformations and moving conductors.
Supervisors: Karel Van Bockstal and Marian Slodička.
For further information about my research and academic activities, please consult the following pages: