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An exact solution of a limit case Stefan problem governed by a fractional diffusion equation. (English) Zbl 1201.80065
Summary: An anomalous diffusion version of a limit Stefan melting problem is posed. In this problem, the governing equation includes a fractional time derivative of order 0<β1 and a fractional space derivative for the flux of order 0<α1. Solution of this fractional Stefan problem predicts that the melt front advance as s=t γ ,γ=β α+1. This result is consistent with fractional diffusion theory and through appropriate choice of the order of the time and space derivatives, is able to recover both sub-diffusion and super-diffusion behaviors for the melt front advance.
MSC:
80A22Stefan problems, phase changes, etc.
26A33Fractional derivatives and integrals (real functions)
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