Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth

Antoine Pauthier and Arnd Scheel

Mathematische Nachrichten, 2020, vol. 293, issue 8, 1565-1590

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.

Date: 2020
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https://doi.org/10.1002/mana.201900159

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