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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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the L[sup 2] decay rates for the solution to a class system of non-Newtonian fluid in R[sup n](n>=2). The decay rates are optimal in the sense that they coincide with the decay rates of the solution to the heat system. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]