Publication Cover
Applicable Analysis
An International Journal
Volume 56, 1995 - Issue 3-4
16
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Periodic solutions of a quasilinear parabolic boundary value problem arising in unsaturated flow through a porous medium

&
Pages 279-301 | Received 28 Dec 1993, Published online: 20 Jan 2011

References

  • Alt , H.W. 1983 . “ Nonsteady fluid flow through porous media ” . In Free boundary , Vol. 120 , 222 – 228 . Boston-London-Melbourne : Pitman .
  • Alt , H.W. and Luckhaus , S. 1983 . Quasilinear elliptic-parabolic differential equations . Math. Z. , 183 : 311 – 341 .
  • Bear , J. 1971 . “ Dynamics of Fluids in Porous Media ” . New-York : Elsevier .
  • Bear , J. and Verruijt , A. 1971 . “ Modelling Groundwater Flow and Pollution ” . D. Reidel Publishing Company .
  • Bénilan , Ph. 1981 . “ Evolution equations and accretive operators ” . In Lecture Notes , Univ. of Kentucky .
  • Bénilan , Ph. and Diaz , J.I. in press . Article in preparation ,
  • DiBenedetto , E. and Friedman , A. 1986 . Periodic behaviour for the evolutionary dam problem and related free boundary problems . Comm. in P.D.E. , 11 ( 12 ) : 1297 – 1377 .
  • Diaz , J.I. and Kersner , R. 1987 . On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium . J. Diff. Eqns. , 69 ( 3 ) : 386 – 403 .
  • Diaz , J.I. and Thelin , F. de . 1994 . On doubly nonlinear parabolic equations arising in some models related to turbulent flows . To appear in SIAM Math. Analysis ,
  • Van Duyn , C.J. and Peletier , L.A. 1992 . Nonstationary filtration in partially saturated porous media . Arch. Rational Mech. Anal. , 78 : 173 – 198 .
  • Friedman , A. 1964 . Partial differential equations of parabolic type , Prentice-Hall .
  • Gilding , B.H. 1977 . A nonlinear degenerate parabolic equation . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 4 ( 4 ) : 393 – 432 .
  • Gilding , B.H. 1989 . Improved theory for a nonlinear degenerate parabolic equation . Ann. Scuola Norm. Sup. Pisa C1. Sci. Serie IV , 16 ( 2 ) : 165 – 224 .
  • Kenmochi , K. , Kröner , D. and Kubo , M. 1990 . Periodic solutions to porous media equations of parabolic-elliptic type . J.P.D.E. , 3 ( 3 ) : 63 – 77 .
  • Kenmochi , N. and Kubo , M. 1989 . Periodic behaviour of solutions to a parabolic-elliptic problem . Recent advances in nonlinear elliptic and parabolic problems , 208 : 68 – 76 . Longman Research Notes in Math.
  • Krasnosel'skii , M.A. 1964 . Positive solutions of operator equations , Groninge Noordhoff .
  • Kröner , D. and Rodrigues , J.F. 1985 . Global behaviour for bounded solutions of a porous media equation of elliptic-parabolic type . J. Math. Pures et Appl. , 64 : 105 – 120 .
  • Ladyzhenskaja , O.A. , Solonnikov , V.A. and Ural'ceva , N.N. 1968 . “ Linear and quasi- linear equations of parabolic type ” . In Trans. Math. Monographs , Vol. 23 , Providence, Rhode Island : Am. Math. Society .
  • Levine , H. and Payne , L. 1974 . Nonexistence theorems for the Heat Equation with Non-linear Boundary Conditions and for the Porous Medium Equation Backward in time . J. Diff. Eq. , 16 : 319 – 334 .
  • Oleinik , O.A. , Kalashnikov , A.S. and Chzhou Lin , Y.L. 1958 . The Cauchy problem . Izv. Akad. Nauk SSSR Ser. Mat. , 22 : 667 – 704 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.