Gabriel Wechter

Scalar conservation laws are first order hyperbolic PDEs widely applied to model the mass conservation of various physical and biological systems. The solution to such an equation exhibits a traveling wave structure that closely relates the time evolution process to its initial condition. However, nonlinear advection in many systems gives rise to major challenges in analyzing the corresponding PDE models. In this talk, we will derive the conservation law from physical principles, and investigate solutions both analytically and numerically.