On the estimates of the rate of stabilization for some problems with free boundary

• Date: 1992
• Main Authors: Bazaly, В. V., Tedeev, A. F., Базалий, Б. В., Тедеев, А . Ф.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8224
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $u_t–u_{xx}+u^{\beta}=0$, $\beta \in (0,1)$, in the case of one geometric variable.