Phase transition for models of an elastic medium with residual stress

A variational problem on martensite-austenite phase transitions in a continuous medium is considered. The energy functional of this problem depends on two parameters: the temperature, which runs all real values, and the positive surface tension coefficient. A half-plane is divided into three open zones. In the first zone, only the martensite one-phase equilibrium state is realized. In the second zone, only the austenite one-phase equilibrium state is realized, whereas, in the third zone, any equilibrium state is a two-phase one. On the interface surfaces separating the zones, only those equilibrium states are realized that are typical for adjoining zones. In the homogeneous and isotropic case, the explicit solution to the problem is given provided that the surface tension coefficient is zero. Bibliography: 12 titles. Illustrations: 4 figures. Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 153–191.