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Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces

We prove the existence of solutions global in time to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear nonuniformly parabolic equation of second order. The problem models the behavior in time of materials with martensitic phase transformations. This model with diffusive phase interfaces was derived from a model with sharp interfaces, whose evolution is driven by configurational forces, and can be considered to be a regularization of that model. Our existence proof, which contributes to the verification of the model, is only valid in one space dimension.