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Elementary solutions of plane nonlinear filtration problems

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Abstract

In the solution of plane problems of filtration theory it is important to study the behavior of the solution near the singular points of the boundary of the flow region (corner points, points of boundary-condition change, and so on) and at infinity (see, for example, [1]). In the present study, this analysis is made for nonlinear filtration problems.

Just as in the analogous problems of gasdynamics [2, 3] and nonlinear elasticity theory [4], to find the singular solutions we make the transformation to the filtration velocity hodograph plane. Examples relating basically to filtration with the limiting gradient are presented.

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References

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Authors and Affiliations

  1. Makhachkala, Moscow

    M. G. Alishaev, V. M. Entov & A. E. Segalov

Authors
  1. M. G. Alishaev
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  2. V. M. Entov
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  3. A. E. Segalov
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Additional information

The authors wish to thank I. I. Eremlna, T. N. Ericheva, and T. N. Ivanova for assistance in the calculations.

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Alishaev, M.G., Entov, V.M. & Segalov, A.E. Elementary solutions of plane nonlinear filtration problems. Fluid Dyn 4, 77–84 (1969). https://doi.org/10.1007/BF01025145

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  • DOI: https://doi.org/10.1007/BF01025145

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