Viscosity solutions to a new phase-field model with Neumann boundary condition for solid-solid phase transitions

Abstract 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.