Improved theory for a nonlinear degenerate parabolic equation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 16 (1989) no. 2, p. 165-224
@article{ASNSP_1989_4_16_2_165_0,
author = {Gilding, B. H.},
title = {Improved theory for a nonlinear degenerate parabolic equation},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 16},
number = {2},
year = {1989},
pages = {165-224},
zbl = {0702.35140},
mrnumber = {1041895},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1989_4_16_2_165_0}
}

Gilding, B. H. Improved theory for a nonlinear degenerate parabolic equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 16 (1989) no. 2, pp. 165-224. http://www.numdam.org/item/ASNSP_1989_4_16_2_165_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, New York (1975). | MR 450957 | Zbl 0314.46030

[2] P. Bénilan, Evolution Equations and Accretive Operators, Lecture Notes taken by S. Lenhart, University of Kentucky (1981), 129 pp.

[3] P. Bénilan - J.I. Diaz, Unpublished notes.

[4] P. Bénilan - H. Touré, Sur l'équation générale ut = Φ(u) xx - ψ(u)x + v, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 919-922. | Zbl 0586.35016

[5] J. Buckmaster, Viscous sheets advancing over dry beds, J. Fluid Mech. 81 (1977), 735-756. | MR 455812 | Zbl 0379.76029

[6] S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Modem Phys. 15 (1943), 1-89. | MR 8130 | Zbl 0061.46403

[7] E.C. Childs, An Introduction to the Physical Basis of Soil Water Phenomena, John Wiley & Sons, London (1969).

[8] J.I. Diaz - R. Kersner, On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium, J. Differential Equations, 69 (1987), 368-403. | MR 903393 | Zbl 0634.35042

[9] C.J. Van Duyn - L.A. Peletier, Nonstationary filtration in partially saturated porous media, Arch. Rational Mech. Anal. 78 (1982), 173-198. | MR 648943 | Zbl 0502.76101

[10] B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc. (2) 13 (1976), 103-106. | MR 399658 | Zbl 0319.35045

[11] B.H. Gilding, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 393-432. | Numdam | MR 509720 | Zbl 0364.35027

[12] B.H. Gilding, The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal. 100 (1988), 243-263. | MR 918796 | Zbl 0672.76094

[13] B.H. Gilding, Localization of solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions, Nonlinear Anal., to appear. | MR 1020728 | Zbl 0698.35077

[14] O.A. Ladyzhenskaja - V.A. Solonnikov - N.N. Ural'Ceva, Linear and Quasi-linear Equations of Parabolic Type, Trans. Math. Monographs 23, American Mathematical Society, Providence, Rhode Island (1968). | Zbl 0174.15403

[15] O.A. Oleinik - A.S. Kalashnikov - Y.-L. Chzhou, The Cauchy problem and boundary problems for equations of the type of non-stationary filtration (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 667-704. | MR 99834

[16] M.H. Protter - H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey (1967). | MR 219861 | Zbl 0153.13602