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.
Original language | English (US) |
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Pages (from-to) | 1565-1590 |
Number of pages | 26 |
Journal | Mathematische Nachrichten |
Volume | 293 |
Issue number | 8 |
DOIs | |
State | Published - Aug 1 2020 |
Bibliographical note
Publisher Copyright:© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords
- advection-diffusion
- convergence
- long time dynamics
- phase diffusion