ap.analysis of pdes – Examples of applications of hyperbolic conservation laws


I am giving a talk in front of my applied PDE research group on hyperbolic conservation laws, the most basic form of which is the PDE $$ u_t + f(u)_x = 0 $$ where $u$ is the conserved quantity and $f$ is the flux. I was asked to present “nice applications” of these, and I thought to ask here. Does anyone here know of “nice” or “useful” applications of these in pure or applied mathematics? Maybe something you use in your own research. I thank all contributors.