Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth
Antoine Pauthier, Arnd Scheel · Mathematische Nachrichten · 2020
Abstract 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.