J. I. Adachi and E. Detournay, Plane-strain propagation of a fluiddriven fracture: finite toughness self-similar solution, Proc. Roy. Soc. London Series A, 1994.

J. I. Adachi and A. P. Peirce, Asymptotic Analysis of an Elasticity Equation for a Finger-Like Hydraulic Fracture, Journal of Elasticity, vol.447, issue.6, pp.90-133, 2008.
DOI : 10.1007/s10659-007-9122-4

G. I. Barenblatt, On some unsteady motions of a liquid and gas in a porous medium, Akad. Nauk SSSR. Prikl. Mat. Meh, vol.16, pp.67-78, 1952.

F. Bernis, L. A. Peletier, and S. M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Anal, pp.217-234, 1992.

P. Biler, C. Imbert, and G. Karch, Barenblatt profiles for a nonlocal porous medium equation, Comptes Rendus Mathematique, vol.349, issue.11-12, pp.349-641, 2011.
DOI : 10.1016/j.crma.2011.06.003

R. M. Blumenthal, R. K. Getoor, and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc, vol.99, pp.540-554, 1961.

S. L. Crouch and A. M. Starfield, Boundary Element Methods in Solid Mechanics, With applications in rock mechanics and geological engineering, 1983.
DOI : 10.1115/1.3167130

J. Desroches, E. Detournay, B. Lenoach, P. Papanastasiou, J. R. Pearson et al., The Crack Tip Region in Hydraulic Fracturing, Proc. R. Soc. Lond. A, pp.447-486, 1994.
DOI : 10.1098/rspa.1994.0127

R. Ferreira and F. Bernis, Source-type solutions to thin-film equations in higher dimensions, European Journal of Applied Mathematics, vol.8, issue.5, pp.507-524, 1997.
DOI : 10.1017/S0956792597003197

D. I. Garagash, Plane-strain propagation of a fluid-driven fracture during injection and shut-in: Asymptotics of large toughness, Engineering fracture mechanics, pp.456-481, 2006.

J. Geertsma and F. De-klerk, A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures, Journal of Petroleum Technology, vol.21, issue.12, pp.1571-1581, 1969.
DOI : 10.2118/2458-PA

C. Imbert and A. Mellet, Existence of solutions for a higher order non-local equation appearing in crack dynamics, Nonlinearity, vol.24, issue.12, pp.24-3487, 2011.
DOI : 10.1088/0951-7715/24/12/008

URL : https://hal.archives-ouvertes.fr/hal-00451017

S. L. Mitchell, R. Kuske, and A. P. Peirce, An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case, Journal of Applied Mechanics, vol.74, issue.2, pp.365-372, 2006.
DOI : 10.1115/1.2200653

A. Peirce, Notes about fractures

A. Peirce and E. Detournay, An implicit level set method for modeling hydraulically driven fractures, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.33-40, pp.2858-2885, 2008.
DOI : 10.1016/j.cma.2008.01.013

A. P. Peirce and E. Siebrits, A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems, International Journal for Numerical Methods in Engineering, vol.39, issue.13, pp.1797-1823, 2005.
DOI : 10.1002/nme.1330

A. P. Peirce and E. Siebrits, An Eulerian finite volume method for hydraulic fracture problems, in Finite volumes for complex applications IV, ISTE, pp.655-664, 2005.

M. Riesz, Integrales de Riemann-Liouville et Potentiels, Acta Litt. Sci. Szeged, vol.9, pp.1-42, 1938.
DOI : 10.1007/978-3-642-37535-4_38

D. A. Spence and P. Sharp, Self-Similar Solutions for Elastohydrodynamic Cavity Flow, Proc. Roy. Soc. London Ser. A, pp.400-289, 1985.
DOI : 10.1098/rspa.1985.0081

Y. B. Zeldovich and A. Kompaneets, Towards a theory of heat conduction with thermal conductivity depending on the temperature, Collection of papers dedicated to 70th birthday of Academician AF Ioffe, Izd. Akad. Nauk SSSR, pp.61-71, 1950.

Y. P. Zheltov and S. A. Khristianovich, On hydraulic fracturing of an oil-bearing stratum, Izv. Akad. Nauk SSSR. Otdel Tekhn. Nauk, vol.5, pp.3-41, 1955.