Geodesic
On the local solvability of the two-dimensional Hele--Shaw problem with fractional derivative with respect to time
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 102-131

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We study the two-dimensional quasistationary Stefan probem (the Hele–Shaw problem) in which the motion of the free boundary is described by a “fractional” Darcy law. We prove the existence and uniqueness of a classical solution to the free boundary problem for a small time interval. 
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     author = {N. V. Vasil'eva and N. V. Krasnoshchek},
     title = {On the local solvability of the two-dimensional {Hele--Shaw} problem with fractional derivative with respect to time},
     journal = {Matemati\v{c}eskie trudy},
     pages = {102--131},
     publisher = {mathdoc},
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N. V. Vasil'eva; N. V. Krasnoshchek. On the local solvability of the two-dimensional Hele--Shaw problem with fractional derivative with respect to time. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 102-131. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a5/