Shock waves in conservation laws: dynamical perspective
(Yulia Petrova) - PUC Rio

Many natural phenomena can be described as propagating fronts: spreading of Aedes mosquitoes in Rio de Janeiro, displacement of oil by water in Buzios oil reservoir, or even the movement of the wine along the edge of the glass (search in YouTube for ”Why does wine cry?”).

From PDEs perspective, such fronts can be approximated by a shock wave in a corresponding system of conservation laws (usually of hyperbolic type) or a travelling wave solution of the reaction-diffusion equations (of parabolic type). From dynamical perspective, these special solutions correspond to heteroclinic orbits for some dynamical systems. We will see this connection on two examples from fluid dynamics: polymer flooding and propagation of viscous / gravitational fingers.