Applied Analysis (AA)
The field of Applied Analysis brings together many mathematical topics, such differential equations, dynamical systems, variational calculus, functional analysis, geometry, and approximation theory. The Applied Analysis Group focuses on the interaction between these mathematical disciplines and the real world around us.
A number of themes are common to much of the research of the group:
- (Nonlinear) partial differential equations: well-posedness and qualitative properties such as parameter dependence and asymptotic behaviour, rigorous convergence analysis of numerical schemes.
- Multiscale problems: homogenization, upscaling, rough and moving boundaries, discrete-to-continuum transitions.
- Variational methods for PDEs: minimization, critical point theory, gradient flows, Gamma-convergence.
While there are many, many different applications, some of the more important application areas are:
- Continuum mechanics: elasticity, viscous flows, reactive flows, plasticity, acoustics, and many others.
- Biology: biochemistry, biophysics, but also agent-based models of groups of people and animals.