| Abstract: |
| Dislocations are important line defects in crystalline materials and play essential roles in understanding materials properties like plastic deformation. In this talk, I will first talk about the static Peierls-Nabarro (PN) models for a single straight/curved dislocation line, which can be reduced to a Ginzburg-Landau equation/systems involving anisotropic half-Laplacian. The existence of local minimizers, uniqueness of stable solution and the exponential relaxation of dynamic solutions to the global minimizer (uniquely determined) will be discussed. |
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