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The asymptotic behaviour of the solution of the filtration equation. (English) Zbl 0254.35054

MSC:
35K05Heat equation
35B40Asymptotic behavior of solutions of PDE
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References:
[1] D. G. Aronson,Regularity properties of flows through porous media, SIAM J. Appl. Math.17 (1969), 461--467. · Zbl 0187.03401 · doi:10.1137/0117045
[2] D. G. Aronson,Regularity properties of flows through porous media, SIAM J. Appl. Math.19 (1970), 299--307. · Zbl 0255.76099 · doi:10.1137/0119027
[3] D. G. Aronson,Regularity properties of flows through porous media: the interface, Arch. Rational Mech. Anal.37 (1970), 1--10. · Zbl 0202.37901 · doi:10.1007/BF00249496
[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). · Zbl 0101.21004
[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).
[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).
[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).
[9] S. L. Sobolev,Application of Functional Analysis in Math. Physics Amer. Math. Soc. Transl. Vol. 7., Providence, R. I., 1963. · Zbl 0123.09003
[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).