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.

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具有非线性边界通量的对流扩散动力学作为晶体生长模型

我们分析了非线性边界条件对半线上的对流扩散方程的影响。我们的模型受到晶体生长模型的启发，其中扩散模拟位移场的扩散弛豫，由顶端生长引起的平流，并且边界条件结合了对边界位移的非绝热效应。该方程，特别是边界通量，具有离散规范对称性，我们研究简单的、完整的解，这里是周期的、同宿的或异宿的，相对于这种规范对称性，在全局动力学中的作用。