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

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  • Antoine Pauthier
  • Arnd Scheel

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.

Suggested Citation

  • Antoine Pauthier & Arnd Scheel, 2020. "Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth," Mathematische Nachrichten, Wiley Blackwell, vol. 293(8), pages 1565-1590, August.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:8:p:1565-1590
    DOI: 10.1002/mana.201900159
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