Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry - Berezovsky, A. A.; Mitropolskiy, Yu. A.; Shkhanukov-Lafishev, M. Kh. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
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 the stabilization time $T$.