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Similar solutions and the asymptotics of filtration equations. (English) Zbl 0336.76036

MSC:
76S05 Flows in porous media; filtration; seepage
35K15 Initial value problems for second-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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[1] Barenblatt, G. I., & Ya. B. Zel’dovich, Self-similar solutions as intermediate asymptotics. Annual Review of Fluid Mech. V. 4, 285–312 (1972). · Zbl 0249.76001 · doi:10.1146/annurev.fl.04.010172.001441
[2] Il’in, A. M., A. S. Kalashnikov, & O. A. Oleinik, Linear second order parabolic equations. Usp. Math. Nauk SSSR, 17, no. 3, 3–146 (1962) (Russian).
[3] Kamenomostskaya, S., The asymptotic behaviour of the solution of the filtration equation. Israel J. of Math. 14, 1, 76–87 (1973). · Zbl 0254.35054 · doi:10.1007/BF02761536
[4] Kamin (Kamenomostskaya), S., Some estimates for solutions of the Cauchy problem for equations of a nonstationary equations. J. Diff. Eq. (to appear).
[5] Oleinik, O. A., A. S. Kalashnikov, & Chzhou, Yui-Lin, The Cauchy problem and boundary problems for equations of the type of non-stationary filtration. Izv. Akad. Nauk SSSR, Ser. Mat. 22, 667–704 (1958) (Rus.)
[6] Peletier, L. A., On the asymptotic behaviour of velocity profiles in laminar boundary layers. Arch. Rational Mech. Anal. 45, 110–119 (1972). · Zbl 0236.76023 · doi:10.1007/BF00253040
[7] Peletier, L. A., Asymptotic behaviour of temperature profiles of a class of non-linear heat conduction problems. Quart. Journ. Mech. Appl. Math., 23, 441–447 (1970). · Zbl 0203.41003 · doi:10.1093/qjmam/23.3.441
[8] Peletier, L. A., Asymptotic behaviour of solutions of the porous media equation. SIAM J. Appl. Math., V. 21, No. 4 (1971). · Zbl 0229.35010
[9] Serrin, J., Asymptotic behaviour of velocity profiles in the Prandtl boundary layer theory. Proc. R. Soc. A299, 491–507 (1967). · Zbl 0149.44901 · doi:10.1098/rspa.1967.0151
[10] Sobolev, S. L., Applications of Functional Analysis in Math. Physics. Amer. Math. Soc. Translations 7. Providence, R.I. (1963).
[11] Zel’dovich, I. B., & A. S. Kompaneez, On the theory of heat propagation with heat conduction depending on temperature: Lectures dedicated on the 70th Anniversary of A. F. Joffe. Akad. Nauk SSSR, 1950 (Russian).
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