Continuity of solutions of the porous media equation

B. H. Gilding; L. A. Peletier

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)

  • Volume: 8, Issue: 4, page 659-675
  • ISSN: 0391-173X

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Gilding, B. H., and Peletier, L. A.. "Continuity of solutions of the porous media equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.4 (1981): 659-675. <http://eudml.org/doc/83872>.

@article{Gilding1981,
author = {Gilding, B. H., Peletier, L. A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {regularity; porous media equations; quasilinear parabolic equations; Cauchy problem; continuity of the solution},
language = {eng},
number = {4},
pages = {659-675},
publisher = {Scuola normale superiore},
title = {Continuity of solutions of the porous media equation},
url = {http://eudml.org/doc/83872},
volume = {8},
year = {1981},
}

TY - JOUR
AU - Gilding, B. H.
AU - Peletier, L. A.
TI - Continuity of solutions of the porous media equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 4
SP - 659
EP - 675
LA - eng
KW - regularity; porous media equations; quasilinear parabolic equations; Cauchy problem; continuity of the solution
UR - http://eudml.org/doc/83872
ER -

References

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  1. [1] D.G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., 17 (1969), pp. 461-467. Zbl0187.03401MR247303
  2. [2] D.G. Aronson - P. Bénilan, Régularité des solutions de l'équation des milieux poreux dans RN, C. R. Acad. Sci. Paris Sér. A, 288 (1979), pp. 103-105. Zbl0397.35034MR524760
  3. [3] D.G. Aronson - L.A. Peletier, Large time behaviour of solutions of the porous medium equation in bounded domains, J. Diff. Eqns., 39 (1981), pp. 378-412. Zbl0475.35059MR612594
  4. [4] L.A. Caffarelli - A. Friedman, Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc., 252 (1979), pp. 99-113. Zbl0425.35060MR534112
  5. [5] B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc., 13 (1976), pp. 103-106. Zbl0319.35045MR399658
  6. [6] O.A. Ladyzhenskaja - V.A. Solonnikov - N.N. Ural'cfva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs 23, American Mathematical Society, Providence, R.I. (1968). Zbl0174.15403
  7. [7] 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
  8. [8] L.A. Peletier, The porous media equation, Applications of Nonlinear Analysis in the Physical Sciences (Eds. H. Amann, N. Bazley, K. Kirchgässner),pp. 229-241, Pitman, London (1981). Zbl0497.76083MR659697
  9. [9] Ya. B. Zel'dovich - A.S. Kompaneec, On the theory of propagation of heat with the heat conductivity depending on the temperature, Collection Commemorating the Seventieth Birthday of Academician A. F. Ioffe, pp. 61-71, Izdat. Akad. Nauk SSSR, Moscow (1950). MR69381

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