On a multidimensional moving boundary problem governed by anomalous diffusion: analytical and numerical study

  • Nataliya Vasylyeva
  • Lyudmyla Vynnytska


We study the anomalous diffusion version of the quasistationary Stefan problem (the fractional quasistationary Stefan problem) in the multidimensional case \({\Omega(t) \subset R^{n},\, n \geq 2}\). This free boundary problem is a mathematical model of a solute drug released from a polymer matrix (\({n = \overline{1,3}}\)). We prove the existence and uniqueness of the classical solution for this moving boundary problem locally in time. A numerical solution is constructed in the two-dimensional case.

Mathematics Subject Classification

Primary 35R35 35C15 Secondary 35B65 35R11 


Quasistationary Stefan problem Anomalous diffusion Caputo derivative Coercive estimates 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Mechanics of NAS of UkraineDonetskUkraine
  2. 2.Simula Research LaboratoryLysakerNorway

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