Improved theory for a nonlinear degenerate parabolic equation

B. H. Gilding

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 2, page 165-224
  • ISSN: 0391-173X

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Gilding, B. H.. "Improved theory for a nonlinear degenerate parabolic equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.2 (1989): 165-224. <http://eudml.org/doc/84051>.

@article{Gilding1989,
author = {Gilding, B. H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {existence and uniqueness theorems; Cauchy problem; Cauchy-Dirichlet problem; boundary value problem; comparison principles; generalized solutions},
language = {eng},
number = {2},
pages = {165-224},
publisher = {Scuola normale superiore},
title = {Improved theory for a nonlinear degenerate parabolic equation},
url = {http://eudml.org/doc/84051},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Gilding, B. H.
TI - Improved theory for a nonlinear degenerate parabolic equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 2
SP - 165
EP - 224
LA - eng
KW - existence and uniqueness theorems; Cauchy problem; Cauchy-Dirichlet problem; boundary value problem; comparison principles; generalized solutions
UR - http://eudml.org/doc/84051
ER -

References

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  3. [3] P. Bénilan - J.I. Diaz, Unpublished notes. 
  4. [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. Zbl0586.35016
  5. [5] J. Buckmaster, Viscous sheets advancing over dry beds, J. Fluid Mech.81 (1977), 735-756. Zbl0379.76029MR455812
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  7. [7] E.C. Childs, An Introduction to the Physical Basis of Soil Water Phenomena, John Wiley & Sons, London (1969). 
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  10. [10] B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc. (2) 13 (1976), 103-106. Zbl0319.35045MR399658
  11. [11] B.H. Gilding, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 393-432. Zbl0364.35027MR509720
  12. [12] B.H. Gilding, The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal.100 (1988), 243-263. Zbl0672.76094MR918796
  13. [13] B.H. Gilding, Localization of solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions, Nonlinear Anal., to appear. Zbl0698.35077MR1020728
  14. [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). Zbl0174.15403
  15. [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. MR99834
  16. [16] M.H. Protter - H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey (1967). Zbl0153.13602MR219861

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