  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. The problem models
the behavior in time of materials in which martensitic phase transitions,
driven by configurational forces, take place, and 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 multidimensional
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 reduced problem is one space dimensional.
