  In the present article, we are interested in an initial boundary value
problem for a coupled system of partial differential equations arising in
martensitic phase transition theory of elastically deformable solid materials,
e.g., steel. This model was proposed and investigated in previous work by Alber
and Zhu in which the weak solutions are defined in a standard way, however the
key technique is not applicable to multi-dimensional problem. Intending to
solve this multi-dimensional problem and to investigate the sharp interface
limits of our models, we thus define weak solutions in a different way by using
the notion of viscosity solution, then prove the existence of weak solutions to
this problem in one space dimension, yet the multi-dimensional problem is still
open.
