CA: Mathematical topics and methods in PDEs from physics and biology

In this course, we will present and discuss various types of models inspired by gas dynamics, evolution of species, fluid mechanics, among others, that consists in partial differential equations. Modelling, qualitative behaviour, quantitative analysis and numerical approaches will be the core of the course. The exact content can be adapted to the audience, but it is plan to review basics on evolution equations, elliptic and hypo elliptic operators and basic numerical schemes.

A tentative bibliography includes

• Tranport equations in biology, by B. Perthame.
• Partial Differential Equations, by L.C. Evans.
• Parabolic equations in biology, by B. Perthame.
• Applied Partial Differential Equations: A Visual Approach, by P. Markowich.