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

Solvability via viscosity solutions for a model of phase transitions driven by configurational forces