| Abstract: | 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. |
