On the estimates of the rate of stabilization for some problems with free boundary - Bazaly, В. V.; Tedeev, A. F. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
With the help of energy estimates we study the behavior of solutions of the Dirichlet problem and the Stefan problem under unbounded growth of time for the semilinear equation $u_t–u_{xx}+u^{β}=0$, $β \in (0,1)$, in the case of one geometric variable.