The Group intends to promote research on different forms of PDEs, through state of the art analytical and numerical methods. When those methods are applied to study a PDE, one is led to understand the underlying phenomenon that this PDE is describing. While the Unit groups colleagues in the Mathematics Department, in line with the interdisciplinary role of PDEs, its outreach extends to other academic units (Physics, Chemistry, Engineering, Economics and Social Sciences, etc.) where it is found that Faculty members are using PDEs as tools for modeling phenomena encountered in their areas of research.
Particular emphasis is put on equations coming from Physics, imaging sciences, and Biology. Current topics of interest include the following:
- Regularity theory for semi-linear and fully nonlinear equations.
- Variational problems related to least gradient functions.
- Inverse problems arising from imaging sciences.
- Mass transport problems and their connections to geometric optics, and data sciences.
- Devising robust algorithms for handling complex computational issues, such as (i) dealing with stable methods to numerically solve problems related to PDEs in general and more specifically to PDEs with singular solutions, and (ii) efficiently implementing parallelism on large scale sparse systems and on time-dependent problems.
Activities, running projects, research networks
- Numerical Stability and Parallel Performance of Enlarged Krylov Subspace Methods (PI Sophie Moufawad, Co-PI Fatima Abu Salem), sponsored by the University Research Board of AUB.
- Comportement en Temps Long des Equations Dispersives Semilinéaires (PI Tristan Roy), sponsored by CEDRE.
- Numerical Approach to Monge-Ampère Equation Appearing in Geometric Optics (PI: Ahmad Sabra), Atiyah UK-Lebanon Fellowship