Interface motion by interface diffusion driven by bulk energy: justification of a diffusive interface model |
| |
Authors: | Hans-Dieter Alber Peicheng Zhu |
| |
Institution: | 1. Fachbereich Mathematik, Technische Universit?t Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany 2. Basque Center for Applied Mathematics (BCAM), Building 500, Bizkaia Technology Park, 48160, Derio, Spain 3. IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
|
| |
Abstract: | We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory
coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges
to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by
interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface
models based on the Cahn–Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian
of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic
solution does not solve the system exactly, the proof is formal. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|