References
S. A. Khristianovich and V. P. Zheltov, in Proc. 4th World Petroleum Congress (Rome, 1955), pp. 579–586.
R. P. Nordgren, Soc. Petroleum Eng. J. 12(8), 306 (1972).
D. A. Spence and P. W. Sharp, Proc. Roy Soc. London, Ser. A 400, 289 (1985).
J. Adachi, E. Siebrits, et al., Int. J. Rock Mech. Mining Sci. 44, 739 (2007).
J. Hu and D. I. Garagash, J. Eng. Mech., ASCE 136(9), 1152 (2010).
J. A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge, Cambridge University Press, 1999), p. 370.
J. Hadamard, Princeton University Bulletin, 1902, pp. 49–52.
A. N. Tychonoff, Soviet Math. 4, 1035 (1963). [A. N. Tikhonov, Dokl. AN SSSR 151, 501 (1963)].
M. M. Lavrent’ev and L. Ya. Savel’ev, Theory of Operators and Ill-Posed Problems (Novosibirsk, Institute of Mathematics im. S.L. Sobolev, 1999), p. 702; ISBN 5-86134-077-3 [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Doklady Akademii Nauk, 2011, Vol. 439, No. 4, pp. 473–475.
The article was translated by the author.
Rights and permissions
About this article
Cite this article
Linkov, A.M. Speed equation and its application for solving ill-posed problems of hydraulic fracturing. Dokl. Phys. 56, 436–438 (2011). https://doi.org/10.1134/S1028335811080015
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335811080015