Forced Burgers equation with sticky impulsion source

Abstract We consider the inviscid Burgers equation with force ∂tu + ∂x(u2/2) = ν, where the discontinuities of initial datum u0 are interpreted as force sources. Thence, ν is the force of shocks in a sticky dynamics of (paradoxically) non accelerated particles, whose the mass distribution field is ∂xu. The force has its own dynamics of density field η = u − w (the experienced impulsion), where w denotes the sticky particle velocity field. Along the sticky particle trajectory t |→ Xt, the processes t |→ η(Xt, t), u(Xt, t), w(Xt, t) are backward martingales. 2010 MSC: 28C05, 35Q35, 35Q53, 76F20, 76F55, 76M35