Kesh Govinder
University of KwaZulu-Natal (UKZN)
Title
A group theoretic approach to underdetermined PDEs
Abstract
Underdetermined partial differential equations arise frequently in Astrophysics as there are often fewer constraints on the evolution of the system than there are unknown functions. As such, it is desirable to find solutions to these equations in a systematic manner. Here, we utilise the group theoretic
approach of Sophus Lie to find such solutions. We will also discuss a different route to solution via partial invariants that realise “generating functions”. Finally, we will comment on the likelihood of reducing the order of these partial differential equations, a concept that usually arises in the solution of ordinary differential equations.
Biography: Kesh Govinder is a Professor of Applied Mathematics. His research interests lie in the field of Differential Equations. He looks both at the analysis of equations (symmetry methods, singularity analysis and dynamical systems analysis) as well as applications in General Relativity (Cosmology and Astrophysics), Financial Mathematics (PDEs) and Mathematical Biology (Epidemiology and Cancer modelling). He has published extensively in internationally recognised journals and been involved in a number of local and international conference presentations as well organising a number of conferences. He is actively involved in supervising postgraduate student and has graduated over 40 MSc and PhD students. He is a regular reviewer for the NRF and has continuously attracted funding. Most recently he has been appointed Co-Editor-in-Chief of the Q1 journal Communications in Partial Differential Equations.