Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy
Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy
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DOI：
10.1137/22m1469791
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发表时间：
2022-01
影响因子：
2
通讯作者：
Yuan Gao;J. Roquejoffre
中科院分区：
文献类型：
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作者：
Yuan Gao;J. Roquejoffre
位错动力学中的非平衡过程及其向亚稳态转变轮廓的弛豫对于理解材料中线缺陷引起的塑性变形是至关重要的。在本文中，我们考虑的二维标量位错模型描述的体扩散方程与界面上的动态边界条件，其中的非凸失配势，由于位错的存在，产生一个界面上的界面反应项。我们证明了这个体-界面耦合系统的动力学解将一致收敛到亚稳跃迁轮廓，该轮廓在远场具有双态和厚尾衰减率。亚稳态模式的这种全局稳定性是第一个结果，仅由滑移面上的界面反应驱动的体界面耦合动力学。
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.