Abstract
By the method of a priori estimates, we establish differential inequalities for energy norms in W 12, r of solutions of problems with free boundary for a one-dimensional evolution equation in a medium with fractal geometry. On the basis of these inequalities, we obtain estimates for the stabilization time T.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 997–1001, July, 2005.
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Mitropol'skii, Y.A., Berezovskii, A.A. & Shkhanukov-Lafishev, M.K. Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry. Ukr Math J 57, 1177–1182 (2005). https://doi.org/10.1007/s11253-005-0254-z
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DOI: https://doi.org/10.1007/s11253-005-0254-z