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

Abstract

We study the anomalous diffusion version of the quasistationary Stefan problem (the fractional quasistationary Stefan problem) in the multidimensional case Ω(t)⊂Rn,n≥2. This free boundary problem is a mathematical model of a solute drug released from a polymer matrix (FOrmula Presented). 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.