论文标题
从金茨堡 - 兰道能量的动态边界反应扩散的渐近稳定性
Asymptotic stability for diffusion with dynamic boundary reaction from Ginzburg-Landau energy
论文作者
论文摘要
位错动力学的非平衡过程及其对亚稳态过渡曲线的松弛对于理解材料线缺陷引起的塑性变形至关重要。在本文中，我们考虑了标量位错模型的全部动力学在二维中，由散装扩散方程与界面上的动态边界条件相连，在界面上，由于脱位的存在，非凸差不拟合电位产生了界面上的界面反应项。我们证明了该大块接口耦合系统的动态解决方案将均匀地收敛到亚稳态过渡曲线，该转型剖面具有在远场的脂肪尾衰减速率的双态。亚稳态模式的这种全局稳定性是仅由滑移平面上的界面反应驱动的块状耦合动力学的第一个结果。
The nonequilibrium process in dislocation dynamics and its relaxation to the metastable transition profile is crucial for understanding the plastic deformation caused by line defects in materials. In this paper, we consider the full dynamics of a scalar dislocation model in two dimensions described by the bulk diffusion equation coupled with dynamic boundary condition on the interface, where a nonconvex misfit potential, due to the presence of dislocation, yields an interfacial reaction term on the interface. We prove the dynamic solution to this bulk-interface coupled system will uniformly converge to the metastable transition profile, which has a bi-states with fat-tail decay rate at the far fields. This global stability for the metastable pattern is the first result for a bulk-interface coupled dynamics driven only by an interfacial reaction on the slip plane.
