Publication Cover
Applicable Analysis
An International Journal
Volume 51, 1993 - Issue 1-4
14
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Existence and regularity theorems for a two-phase degenerate stefan problem with convection

Pages 221-250 | Received 05 Sep 1991, Published online: 02 May 2007

References

  • Atthey , D.R. 1974 . A finite difference scheme for melting problems . J. Inst. Maths. Applics. , 13 : 353 – 366 .
  • Crowley , A.B. 1979 . On the weak solution of moving boundary problem, . J. Inst. Math. Appl., , 24 : 43 – 57 .
  • CANNON , J.R. and Yin , Hong-Ming . 1988 . On the existence of the weak solution and the regularity of the free boundary to a one-dimensional two-phase Stefan problem, . J. Differential Equations, , 73 : 104 – 118 .
  • Van Duyn , C.J. and Peletier , L.A. 1982 . Nonstationary filtration in partially saturated porous media, . Arch. Rational Mech. Anal., , 78 : 173 – 198 .
  • Fasano , A. , Primicerio , M. and Kamin , S. 1977 . Regularity of weak solutions of one-dimensional two-phase Stefan problems, . Ann. Mat. .Pura Appl., , 115 : 341 – 348 .
  • Gilding , B.H. 1989 . Improved theorem for a nonlinear degenerate parabolic equation, . Ann. Scuola Norm. Sup. Pisa C1. Sci., , 16 : 165 – 224 .
  • Gilding , B.H. 1976 . Holder continuity of solutions of parabolic equations, . J. London Math. Soc., , 13 : 103 – 106 .
  • Kamenomostskaya , S.L. 1961 . On the Stefan problem, . Mat. Sbornik, , 53 : 489 – 514 .
  • Lacey , A.A. and Shillor , M. 1983 . The existence and stability of regions with superheating in the classical two-phase one-dimensional Stefan problem with heat sources, . IMA J. Appl. Math., , 30 : 215 – 230 .
  • Solonnikov V.A. Ladyzhenskaya O.A. Uralceva N.N. Linear and quasilinear equation of parabolic type AMS Translations 1969
  • Matano , H. 1982 . “ Nonincrease of the lap‐number of a solution for a one‐dimensional semilinear parabolic equation, ” . Vol. 29 , 401 – 441 . Tokyo Sect. : Pub. Fac. Sci. Univ. .
  • Niezggodka , M. 1983 . “ Stefan-like problems, in Free Boundary Problems: ” . In Theory and Applications, , Edited by: Fasano et al , A. Vol. 79 , 321 – 348 . London : Pitman .
  • Rubinstein , L.I. 1971 . “ The Stefan Problem, ” . In AMS Trans. Math. Monograms , Vol. 27 , Rhode Island : Providence .
  • Xu , X. 1990 . Regularity results for a one-dimensional two‐phase degenerate Stefan problem, . J. Differential Equations, , 87 : 96 – 114 .
  • Xu , X. 1991 . On the regularity of weak solutions of a one‐dimensional twophase degenerate Stefan problem with convection, . J. Differential Equations, , 91 : 53 – 77 .
  • Xu , X. 1991 . A diffusion problem involving two free boundaries, . Rend. Circ. Mat. Palermo, Ser II, , 40 : 69 – 101 .

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.