Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry

• Date: 2005
• Main Authors: Berezovsky, A. A., Mitropolskiy, Yu. A., Shkhanukov-Lafishev, M. Kh., Березовский, А. А., Митропольский, Ю. А., Шхануков-Лафишев, М. Х.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3658
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

By using the method of a priori estimates, we establish differential inequalities for energetic norms in $W^l_{2,r}$ of solutions of problems with a free bound in media with the fractal geometry for one-dimensional evolutionary equation. On the basis of these inequalities, we obtain estimates for...