  We analyze the effect of nonlinear boundary conditions on an
advection-diffusion equation on the half-line. Our model is inspired by models
for crystal growth where diffusion models diffusive relaxation of a
displacement field, advection is induced by apical growth, and boundary
conditions incorporate non-adiabatic effects on displacement at the boundary.
The equation, in particular the boundary fluxes, possesses a discrete gauge
symmetry, and we study the role of simple, entire solutions, here periodic,
homoclinic, or heteroclinic relative to this gauge symmetry, in the global
dynamics.
