[Author] V. G. Osmolovskii [Title] Quasistationary Probem on the Phase Transition of Continuum Mechanics. One-dimensional Case. Zero Coefficient Surface Tension. [AMS Subj-class] 74N15 Analysis of microstructure 49J15 Methods involving semicontinuity and convergence; relaxion. 35R35 Free boundary problems. [Abstract] One-dimensional quasistatinary problem on the phase transition in continuum mechanics is investigated. [Keywords] phase transitions, nonconvex variational problems, free boundary [Comments] Russian, 12 pp. [Contact e-mail] vicos@VO8167.spb.edu