Spherically symmetric solutions to a model for phase transitions driven by configurational forces
We prove the global-in-time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, non-uniformly parabolic equation of second order. This problem models the evolutional behavior of materials in which martensitic phase transitions, driven by configurational forces, take place. Moreover, it can be considered to be a regularization of the corresponding sharp interface model. By assuming that the solutions are spherically symmetric, we reduce the original multi-dimensional problem to the one in one space dimension, then prove the existence of spherically symmetric solutions. Our proof is valid due to the essential feature that the resulting problem is one-dimensional.