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A necessary and sufficient condition for the existence of an interface in flows through porous media. (English) Zbl 0294.35040


MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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[1] Atkinson, F.V., & L.A. Peletier, Similarity solutions of the non-linear diffusion equation. Arch. Rational Mech. Anal. (To appear). · Zbl 0293.35039
[2] Oleinik, O.A., A.S. Kalashnikov & Chzou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration. Izvestija Akademii Nauk SSSR, ser. mat. 22, 667–704 (1958).
[3] Oleinik, O.A., & S.N. Kruzhkov, Quasilinear second order parabolic equations with many independent variables. Russian Math. Surveys 16, 105–146 (1961). · Zbl 0112.32604
[4] Protter, M.H., & H.F. Weinberger, Maximum principles in differential equations. Englewood Cliffs, N.J.: Prentice Hall 1967. · Zbl 0153.13602
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