D. E. Pelinovsky and B. de Rijk
Extinction of multiple shocks in the modular Burgers equation
Nonlinear Dyn 111 (2023) 3679-3687
Abstract:
We consider multiple shock waves in the Burgers' equation with a modular
advection term. It was previously shown that the modular Burgers' equation admits
a traveling viscous shock with a single interface, which is stable against smooth and
exponentially localized perturbations. In contrast, we suggest in the present work 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. We
formulate a precise scaling law of the finite-time extinction supported by the interface
equations and by numerical simulations.
Keywords:
modular Burgers equation; viscous shocks; finite-time extinction; traveling waves; energy estimates;