Caffarelli, Luis A.; Friedman, Avner Continuity of the density of a gas flow in a porous medium. (English) Zbl 0425.35060 Trans. Am. Math. Soc. 252, 99-113 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 56 Documents 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 Keywords:gas flow in a porous medium; degenerate nonlinear parabolic equation; unique generalized solution × Cite Format Result Cite Review PDF Full Text: DOI References: [1] D. G. Aronson, Regularity propeties 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: A counterexample., 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] D. G. Aronson and P. Benilan, Régularité des solutions de l’équation des milieux porous dans \( {R^N}\), C. R. Acad. Sci. Paris, 1979. [5] B. H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc. (2) 13 (1976), no. 1, 103 – 106. · Zbl 0319.35045 · doi:10.1112/jlms/s2-13.1.103 [6] S. Kamenomostskaya, The asymptotic behavior of the solution of the filtration equation, Israel J. Math. 14 (1973), 76 – 87. · Zbl 0254.35054 · doi:10.1007/BF02761536 [7] Barry F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), no. 2, 381 – 415. · Zbl 0365.35030 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.