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The anomalous exponent of the Barenblatt equation

Published online by Cambridge University Press:  26 September 2008

L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands

Abstract

The self-similar source solution of the Barenblatt equation for elasto-plastic filtration through porous rock is known to be of the second kind. We determine the behaviour of the associated anomalous exponent and the profile of the solution in the limit of large compressibility and small elastic recovery of the rock.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Barenblatt, G. I. 1979 Similarity, Self-similarity, and Intermediate Asymptotics. Consultants Bureau, New York.CrossRefGoogle Scholar
[2]Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1972 Theory of Unsteady Filtration of Fluids and Gases. Nedra, Moscow (in Russian).Google Scholar
[3]Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows through Natural Rocks. Kluwer.CrossRefGoogle Scholar
[4]Barenblatt, G. I. & Krylov, A. P. 1955 On elasto-plastic regime of filtration. Izv. Akad. Nauk SSSR, 2, 1426.Google Scholar
[5]Kamenomostkaya, S. L. (Kamin, S.) 1957 On a problem in the theory of filtration. Doklady Akad. Nauk USSR 116, 1820.Google Scholar
[6]Kamenomostkaya, S. L. (Kamin, S.) 1969 Equation of elastoplastic mode of filtration. Appl. Math. Mech. 33, 10421049 (translated from Russian PMM, 1076–1084).CrossRefGoogle Scholar
[7]Kamin, S., Peletier, L. A. & Vazquez, J. L. 1991 On the Barenblatt equation of elasto-plastic filtration. Indiana Univ. Math. J. 40, 13331362.CrossRefGoogle Scholar
[8]Barenblatt, G. I. & Sivashinsky, G. I. 1969 Self-similar solutions of the second kind in nonlinear filtration. Appl. Math. Mech. PMM 33, 836845.CrossRefGoogle Scholar
[9]Aronson, D. G. & Vazquez, J. L. 1994 Calculation of anomalous exponents in nonlinear diffusion. Phys. Rev. Lett. 72, 348351.Google Scholar
[10]Goldenfeld, N., Martin, O., Oono, Y. & Liu, F. 1990 Anomalous dimensions and the renormalization group in a nonlinear diffusion. Phys. Rev. Lett. 64, 13611364.CrossRefGoogle Scholar
[11]M., Abramowitz & Stegun, I. A. (eds.) 1970 Handbook of Mathematical Functions, 9th ed.Dover.Google Scholar