A nonlinear degenerate parabolic equation

B. H. Gilding

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1977)

  • Volume: 4, Issue: 3, page 393-432
  • ISSN: 0391-173X

How to cite


Gilding, B. H.. "A nonlinear degenerate parabolic equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.3 (1977): 393-432. <http://eudml.org/doc/83757>.

author = {Gilding, B. H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {393-432},
publisher = {Scuola normale superiore},
title = {A nonlinear degenerate parabolic equation},
url = {http://eudml.org/doc/83757},
volume = {4},
year = {1977},

AU - Gilding, B. H.
TI - A nonlinear degenerate parabolic equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1977
PB - Scuola normale superiore
VL - 4
IS - 3
SP - 393
EP - 432
LA - eng
UR - http://eudml.org/doc/83757
ER -


  1. [1] F.V. Atkinson - L.A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal., 54 (1974), pp. 373-392. Zbl0293.35039MR344559
  2. [2] J. Bear, Dynamics of fluids in porous media, American Elsevier, New York (1972). Zbl1191.76001
  3. [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. Zbl0231.47034MR273468
  4. [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. Zbl0278.47033MR394323
  5. [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. Zbl0177.37403MR190546
  6. [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. Zbl0191.11602MR241823
  7. [7] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N. J. (1964). Zbl0144.34903MR181836
  8. [8] B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc., 13 (1976), pp. 103-106. Zbl0319.35045MR399658
  9. [9] B.H. Gilding, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal. (to appear). Zbl0366.76074MR447847
  10. [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. Zbl0336.76037MR408428
  11. [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. Zbl0158.11502MR164145
  12. [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. [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). Zbl0174.15403
  14. [14] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Yillars (1969). Zbl0189.40603MR259693
  15. [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. Zbl0093.10302MR99834
  16. [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. Zbl0294.35040MR417572
  17. [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. Zbl0309.35041MR422867
  18. [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. Zbl0153.42202MR215544
  19. [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. Zbl0101.21101MR158190
  20. [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. Zbl0181.37601MR264232

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