Curvature Flow of Networks with Triple Junction Drag and Grain Rotation

Abstract: We prove a local existence result for a PDE system that describes curvature motion of networks with a dynamic boundary condition known as triple junction drag. This model arises in the study of grain boundary evolution in polycrystalline materials. We demonstrate the possibility of a new type of topological change during the evolution of the network. Moreover, we adopt a dynamic surface tension model that depends on the crystallographic orientations of the grains, which are allowed to rotate. Lastly, we study how the stability of stationary solutions depend on the choice of surface tension.