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We prove the global in time existence of spherically symmetric solutions toan initial-boundary value problem for a system of partial differentialequations, which consists of the equations of linear elasticity and anonlinear, non-uniformly parabolic equation of second order. The problem modelsthe behavior in time of materials in which martensitic phase transitions,driven by configurational forces, take place, and can be considered to be aregularization of the corresponding sharp interface model. By assuming that thesolutions are spherically symmetric, we reduce the original multidimensionalproblem to the one in one space dimension, then prove the existence ofspherically symmetric solutions. Our proof is valid due to the essentialfeature that the reduced problem is one space dimensional.

Spherically symmetric solutions to a model for phase transitions driven by configurational forces