Geodesic
Models of plane fractures expansion
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 165-178

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Approximate models of crack opening in the reservoir under the action of the filtered fluid are derived. The cross-sections of the fracture are assumed to be plane-parallel and have a small thickness. The models are based on exact solutions of the equations for viscous fluid motion including invariant solutions. Filtration of a fluid through a moving boundary, the absence of a tangential motion at the boundary, and elastic forces compressing the crack are taken into account.
Keywords: filtration, moving boundary, viscous fluid, exact solutions, fracture expansion. 
@article{CHFMJ_2019_4_2_a3,
     author = {S. V. Khabirov and S. S. Khabirov},
     title = {Models of plane fractures expansion},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {165--178},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a3/}
}
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S. V. Khabirov; S. S. Khabirov. Models of plane fractures expansion. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 165-178. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a3/