Global solutions to a model with Dirichlet boundary conditions for interface motion by interface diffusion. (English) Zbl 1446.82059
Summary: We prove the global existence of weak solutions to an initial-boundary value problem for a new phase-field model, which is a system consisting of a degenerate parabolic equation of fourth-order for an order parameter coupled to a linear elasticity sub-system. This model is applied to describe, at the mesoscopic scale, the motion of grain boundaries in elastically deformable solids. One typical example of this process is sintering. The boundary conditions for this order parameter are of Dirichlet type.
©2020 American Institute of Physics
©2020 American Institute of Physics
MSC:
| 82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 35K55 | Nonlinear parabolic equations |
| 35K65 | Degenerate parabolic equations |
| 74A50 | Structured surfaces and interfaces, coexistent phases |
| 74B10 | Linear elasticity with initial stresses |
| 35G16 | Initial-boundary value problems for linear higher-order PDEs |
| 35D30 | Weak solutions to PDEs |
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