Viscosity solutions to a new phase-field model with Neumann boundary condition for solid-solid phase transitions. (English) Zbl 1444.35091
Summary: We shall study an initial-boundary value problem of a new phase field model, which is a degenerate parabolic equation coupled to a linear elasticity sub-system, used to describe the solid-solid phase transitions in elastically deformable solid materials. We establish a series of approximate solutions to the initial boundary value problem, and prove that the viscosity solutions to this initial boundary value problem exist, in a one dimensional case.
MSC:
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 74N15 | Analysis of microstructure in solids |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
elliptic-parabolic system; degenerate parabolic equation; viscosity solutions; Neumann boundary condition; phase-field model; solid-solid phase transitionsReferences:
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