Geodesic
Mathematical models of a hydraulic shock in a slightly viscous liquid
Matematičeskoe modelirovanie, Tome 24 (2012) no. 5, pp. 112-130

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In the present work are derive two mathematical models, describing the pressure distribution field in the layer near the borehole in process of the hydraulic fracturing. The derivation of the models is based on a rigorous homogenization of the exact mathematical model, governing on microscopic level the joint motion of an elastic solid skeleton and a viscous fluid filling the pores.
Keywords: hydraulic shock, Stokes and Lame's equations, two-scale convergence. 
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     author = {A. M. Meirmanov and I. V. Nekrasova},
     title = {Mathematical models of a hydraulic shock in a slightly viscous liquid},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_5_a8/}
}
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A. M. Meirmanov; I. V. Nekrasova. Mathematical models of a hydraulic shock in a slightly viscous liquid. Matematičeskoe modelirovanie, Tome 24 (2012) no. 5, pp. 112-130. http://geodesic.mathdoc.fr/item/MM_2012_24_5_a8/