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.
Analysis and Partial Differential Equations (APDE) Ghent University
The project will be concentrating on developing different directions of analysis (microlocal analysis, harmonic analysis, time-frequency analysis, spectral analysis) and their interplay among themselves but, most importantly, with the theory of partial differential equations.
Robust optimization of systems described by partial differential equations KU Leuven
Many complex systems and physical phenomena can be modeled by a partial differential equation (PDE). Methods to obtain a numerical solution for a given input are well established. An important engineering problem is to find the input such that the solution is optimal. This requires the definition and minimization of a cost which depends on the control input and the PDE solution. However, models of real-world systems often contain ...
Turning redundancy into a computational advantage: frame-based discretisations of differential equations KU Leuven
Many processes in science and technology are described by mathematical models and equations. The equations capture the physical constraints of the process, and their solutions describe the actual outcomes. Sometimes these equations can be solved by hand, but in modern research more and more scientists rely on numerical computations with a fast computer. Most equations take the form of differential equations. These describe the way a system ...
Transseries and superexact asymptotics in ordinary and partial differential equations Hasselt University
Combining mathematics and physics beyond the introductory level: the case of partial differential equations KU Leuven
Using mathematics in physics requires more than straightforward application of mathematical procedures. But how do students give physical meaning to a mathematical structure? How do they associate mathematical understanding to a physical phenomenon especially at the advanced undergraduate level? It has been proven this is a challenge for learners at all levels of education. In this project we bring together expertise from physics and ...
Transseries and superexact asymptotics in ordinary and partial differential equations Hasselt University
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.