Monday 10th of October 2022, 14:00-15:00 in HG03.085
Victor Hissink Muller
Energy methods in PDEs.
The classical approach to studying partial differential equations (PDEs) from the 18th and 19th centuries is obtaining explicit solutions and analysing these functions to discover interesting properties. However, modern PDE theory developed in the 20th century relies on results in Function Analysis (FA) to prove the existence of solutions to PDEs with a more general concept of solutions. We consider a simple example of a linear elliptic PDE and discuss the FA machinery needed to prove the existence result. The technique is called the energy method and has many generalisations, for instance for hyperbolic and parabolic equations including non-linear terms.