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The asymptotic behaviour of the solution of the filtration equation

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Abstract

It is proved that the self-similar solution of the nonlinear equation of filtration gives the asymptotic representation of the solution of the Cauchy problem for the same equation.

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References

  1. D. G. Aronson,Regularity properties of flows through porous media, SIAM J. Appl. Math.17 (1969), 461–467.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. G. Aronson,Regularity properties of flows through porous media, SIAM J. Appl. Math.19 (1970), 299–307.

    Article  MathSciNet  Google Scholar 

  3. D. G. Aronson,Regularity properties of flows through porous media: the interface, Arch. Rational Mech. Anal.37 (1970), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. I. Barenblatt and I. B. Zeldovich,About the asymptotic properties of the selfsimilar solutions of the equations of unsteady filtration, Dokl. Akad. Nauk SSSR 118,4 (1958), 671–674 (Russian).

    Google Scholar 

  5. A. S. Kalasnikov,The Cauchy problem in the class of increasing functions for equations of non-stationary filtration type, Vestnik Moskov. Univ. Ser. I Mat. Meh.6 (1963) 17–27 (Russian).

    MathSciNet  Google Scholar 

  6. O. A. Oleinik,On some degenerate quasilinear parabolic equations, Seminari dell’ Istituto Nazionalle di Alta Mathematica 1962–63, Oderisi, Gublio, 1964, pp. 355–371.

  7. O. A. Oleinik, A. S. Kalasnikov and Czou, Yui-Lin,The Cauchy problem and boundary problems for equations of the type of non-stationary filtration, Izv. Akad. Nauk SSSR Ser. Mat.22 (1958), 667–704 (Russian).

    MathSciNet  Google Scholar 

  8. O. A. Oleinik and T. D. Ventcel,The first boundary problem and the Cauchy problem for quasi-linear equations of parabolic type. Mat. Sb.41 (83) (1957), 105–128 (Russian).

    MathSciNet  Google Scholar 

  9. S. L. Sobolev,Application of Functional Analysis in Math. Physics Amer. Math. Soc. Transl. Vol. 7., Providence, R. I., 1963.

  10. I. B. Zeldovich and A. S. Kompaneez,On the theory of heat propagation with heat conduction depending on temperature, Lectures dedicated on the 70th Anniversary of A. F. Ioffe, Akad. Nauk SSSR, 1950, (Russian).

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  1. Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    S. Kamenomostskaya

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  1. S. Kamenomostskaya
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Kamenomostskaya, S. The asymptotic behaviour of the solution of the filtration equation. Israel J. Math. 14, 76–87 (1973). https://doi.org/10.1007/BF02761536

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  • DOI: https://doi.org/10.1007/BF02761536

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