Projects
Analysis and Partial Differential Equations Ghent University
The analysis of partial differential equations (PDEs) occupies a central place among a wide range of sciences. Processes of evolution or static models, starting from the groundbreaking works of Isaac Newton, are described by PDEs of different types. The project aims at pursuing their mathematical analysis: frame decompositions, noncommutative analysis, equations with singularities, evolution PDEs, fractional analysis and inverse problems.
Combining mathematics and physics beyond the introductory level: the case of partial differential equations KU Leuven
Theoretical and numerical analysis of inverse problems in evolutionary partial differential equations Ghent University
The aim of this project is a theoretical and numerical study of inverse problems for nonlinear
evolution equations of parabolic and hyperbolic type. The added value relies on the
development of new robust and efficient numerical techniques for inverse problems
containing nonlocal terms.
Novel time integration for partial differential equations Hasselt University
Special Research Fund Professorship in partial differential equations Ghent University
A professorship granted by the Special Research Fund is a primarily research-oriented position and is made available for excellent researchers with a high-quality research programme.
Mathematical and numerical analysis of partial differential equations with a time dependent boundary condition Ghent University
Many physical phenomena ( thermoelasticity, flow in porous media, electromegnetism,U+2026) are modeled by conclassical initial boundary condition. We aim to develop new innovative numerical schemes for such type of problems.
Micro-macro acceleration and multilevel Monte Carlo methods for kinetic equations KU Leuven
Since the 1960's people have made regular claims to the effect of: "A working nuclear fusion reactor is 20 years away!" This persistent underestimaton of the challenges in the way of building a working fusion reactor can be explained by the following dichotomy between theory and practice: On the one hand, the physical reaction is, in principle, quite simple, i.e., heat hydrogen gas to the point where it ionizes and the ions collide with ...
Coping with redundancy: frame-based discretizations of operator equations. KU Leuven
Solutions of generalized Cauchy-Riemann equations in Clifford analysis Ghent University
Complex analysis in the plane studies solutions of a 2x2 system of partial differential equations, called Cauchy-Riemann equations, splitting the Laplacian. Clifford analysis provides a generalization of this system to higher dimension and is nowadays a well-established function theory. This project studies a modification of it by considering transformations of the Cauchy-Riemann equations which split a non-scalar second order operator.