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Continuity of the density of a gas flow in a porous medium. (English) Zbl 0425.35060

MSC:
35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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[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 · doi.org
[4] D. G. Aronson and P. Benilan, Régularité des solutions de l’équation des milieux porous dans \( {R^N}\), C. R. Acad. Sci. Paris, 1979.
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[8] O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Trans. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, R. I., 1968.
[9] Olga Oleĭnik, On some degenerate quasilinear parabolic equations, Seminari 1962/63 Anal. Alg. Geom. e Topol., Vol. 1, Ist. Naz. Alta Mat., Ediz. Cremonese, Rome, 1965, pp. 355 – 371.
[10] O. A. Oleĭnik, A. S. Kalašinkov, and Yuĭ-Lin\(^{\prime}\) Čžou, 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). · Zbl 0093.10302
[11] E. S. Sabinina, On the Cauchy problem for the equation of nonstationary gas filtration in several space variables, Soviet Math. Dokl. 2 (1961), 166 – 169. · Zbl 0101.21101
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