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Some estimates for solution of the Cauchy problem for equations of a nonstationary filtration. (English) Zbl 0318.35048

MSC:
35K55 Nonlinear parabolic equations
35B45 A priori estimates in context of PDEs
35K15 Initial value problems for second-order parabolic equations
76S05 Flows in porous media; filtration; seepage
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[2] Aronson, D.G., Regularity properties of flows through porous media, SIAM J. appl. math., 19, 299-307, (1970) · Zbl 0255.76099
[3] Aronson, D.G., Regularity properties of flows through porous media: the interface, Arch. rational mech. anal., 37, 1-10, (1970) · Zbl 0202.37901
[4] Friedman, A., Partial differential equations of parabolic type, (1964), Prentice-Hall Englewood Cliffs, N.J · Zbl 0144.34903
[5] Kalashnikov, A.S., On the occurance of singularities in the solutions of the equations of nonstationary filtration, Ž. vyčisl. mat. i mat. fiz., 440-444, (1967)
[6] Kalashnikov, A.S., The Cauchy problem in a class of growing functions for equations of unsteady filtration type, Vestnik moskov. univ. ser. VI mat. mech., 6, 17-27, (1963) · Zbl 0158.11502
[7] \scS. Kamin (Kamenomostskaya), Similar solutions as asymptotics for the solutions of the filtration equations, Arch. Rational Mech. Anal., to appear.
[8] Oleinik, O.A.; Kalashnikov, A.S.; Chzhou, Y.L., The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. akad. nauk SSSR ser. mat., 22, 667-704, (1958) · Zbl 0093.10302
[9] Sobolev, S.L., ()
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