I will review the state of art in analysis and modeling of the Burgers’ equation with a modular advection term. The modular Burgers’ equation admits a traveling viscous shock with a single interface, which is stable against smooth and exponentially localized perturbations. In contrast, it can be shown with the help of energy estimates and numerical simulations that the evolution of shock waves with multiple interfaces leads to finite-time coalescence of two consecutive interfaces. A precise scaling law of the finite-time extinction is supported by the interface equations and by numerical simulations.