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

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.

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Bibliographic Details
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
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal