A nonlinear degenerate parabolic equation

Gilding, B. H.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 4 (1977) no. 3, pp. 393-432.

[1] F.V. Atkinson - L.A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal., 54 (1974), pp. 373-392. | MR | Zbl

[2] J. Bear, Dynamics of fluids in porous media, American Elsevier, New York (1972).

[3] H. Brezis, On some degenerate nonlinear parabolic equations, Nonlinear Functional Analysis, Proceedings of Symposia in Pure Mathematics, vol. 18, part 1, American Mathematical Society, Providence, R. I. (1970), pp. 28-38. | MR | Zbl

[4] H. Brezis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Nonlinear Functional Analysis, edited by E. H. Zarantonello, Academic Press, New York (1971), pp. 101-156. | MR | Zbl

[5] Ju A. Dubinskii, Weak convergence in nonlinear elliptic and parabolic equations, Mat. Sb., 67 (1965), pp. 609-642; Amer. Math. Soc. Transl., 67 (1968), pp. 226-258. | MR | Zbl

[6] M.I. Freidlin, Existence « in the large » of smooth solutions of degenerate quasilinear equations, Mat. Sb., 78 (1969), pp. 332-348; Math. USSR-Sb., 7 (1969), pp. 323-339. | MR | Zbl

[7] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N. J. (1964). | MR | Zbl

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

[9] B.H. Gilding, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal. (to appear). | MR | Zbl

[10] B.H. Gilding - L.A. Peletier, The Cauchy problem for an equation in the theory of infiltration, Arch. Rational Mech. Anal., 61 (1976), pp. 127-140. | MR | Zbl

[11] A.S. Kalashnikov, The Cauchy problem in a class of growing functions for equations of unsteady filtration type, Vestnik Moscov. Univ. Ser. I Mat. Meh., 18 (1963), pp. 17-27. | MR | Zbl

[12] A.S. Kalashnikov, On the character of the propagation of perturbations in processes described by quasilinear degenerate parabolic equations, Proceedings of Seminars dedicated to I. G. Petrovskogo, Otdel'nyi ottisk, Moscow (1975), pp. 135-144.

[13] O.A. Ladyzhenskaja - V.A. Solonnikov - N.N. Ural'Ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol. 23, American Mathematical Society, Providence, R. I. (1968). | Zbl

[14] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Yillars (1969). | MR | Zbl

[15] O.A. Oleinik - A.S. Kalashnikov - Chzhou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of unsteady filtration, Izv. Akad. Nauk SSSR Ser. Mat., 22 (1958), pp. 667-704. | MR

[16] L.A. Peletier, A necessary and sufficient condition for the existence of an interface in flows through porous media, Arch. Rational Mech. Anal., 56 (1974), pp. 183-190. | MR | Zbl

[17] L.A. Peletier, On the existence of an interface in nonlinear diffusion processes, Ordinary and Partial Differential Equations, Lecture Notes in Mathematics 415, Springer-Verlag, Berlin (1974), pp. 412-416. | MR | Zbl

[18] P.A. Raviart, Sur la résolution et l'approximation de certaines équations paraboliques non linéaires dégénérées, Arch. Rational Mech. Anal., 25 (1967), pp. 64-80. | MR | Zbl

[19] E.S. Sabinina, On the Cauchy problem for the equation of nonstationary gas filtration in several space variables, Dokl. Akad. Nauk SSSR, 136 (1961), pp. 1034-1037; Soviet Math. Dokl., 2 (1961), pp. 166-169. | MR | Zbl

[20] A.I. Vol'Pert - S.I. Hudjaev, Cauchy's problem for degenerate second order quasilinear parabolic equations, Mat. Sb., 78 (1969), pp.374-396; Math. USSR-Sb., 7 (1969), pp. 365-387. | MR | Zbl