Solutions to a model for interface motion by interface diffusion
Solutions to a model for interface motion by interface diffusion
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DOI：
10.1017/s0308210507000170
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发表时间：
2007-08
期刊：
影响因子：
--
通讯作者：
P. Zhu
中科院分区：
文献类型：
--
作者：
P. Zhu
证明了描述弹性变形固体中界面的相场模型弱解的存在性，该模型是原子沿着界面扩散而运动的。由界面分隔的不同区域的体积是守恒的，因为没有发生穿过界面的原子交换。扩散仅由体自由能的减少驱动。在这个模型中的序参数的演变是由一个退化的抛物型四阶方程。如果这个方程中的正则化参数趋于零，则解趋于界面扩散的尖锐界面模型的解。存在性证明仅对1½维情形有效。
Existence of weak solutions is proved for a phase field model describing an interface in an elastically deformable solid, which moves by diffusion of atoms along the interface. The volume of the different regions separated by the interface is conserved, since no exchange of atoms across the interface occurs. The diffusion is driven only by reduction of the bulk free energy. The evolution of the order parameter in this model is governed by a degenerate parabolic fourth-order equation. If a regularizing parameter in this equation tends to zero, then solutions tend to solutions of a sharp interface model for interface diffusion. The existence proof is valid only for a 1½-dimensional situation.