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Analyticity of the free boundary for the Stefan problem

  • Avner Friedman
Article

Keywords

Neural Network Complex System Nonlinear Dynamics Free Boundary Electromagnetism 
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References

  1. 1.
    Cannon, J.R., & C.D. Hill, On the infinite differentiability of the free boundary in the Stefan problem. J. Math. Anal. Appl. 22, 385–397 (1968).Google Scholar
  2. 2.
    Cannon, J.R., D. Henry & D.B. Kotlow, Continuous differentiability of the free boundary for weak solutions of the Stefan problem. Bull. Amer. Math. Soc. 80, 45–48 (1974).Google Scholar
  3. 3.
    Cannon, J.R., D. Henry & D.B. Kotlow, Classical solutions of the one-dimensional two-phase Stefan problem. To appear.Google Scholar
  4. 4.
    Friedman, A., On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations. J. Math. and Mech. 7, 43–59 (1958).Google Scholar
  5. 5.
    Friedman, A., Free boundary problems for parabolic equations I: Melting of solids. J. Math. and Mech. 8, 499–517 (1959).Google Scholar
  6. 6.
    Friedman, A., Partial Differential Equations of Parabolic Type. Englewood Cliffs, N.J.: Prentice-Hall 1964.Google Scholar
  7. 7.
    Friedman, A., One dimensional Stefan problems with non-monotone free boundary. Trans. Amer. Math. Soc. 133, 89–114 (1968).Google Scholar
  8. 8.
    Friedman, A., Partial Differential Equations. New York: Holt, Rinehart and Winston 1969.Google Scholar
  9. 9.
    Friedman, A., Parabolic variational inequalities in one space dimension and the smoothness of the free boundary. J. Funct. Anal. 18, 151–176 (1975).PubMedGoogle Scholar
  10. 10.
    Friedman, A., & R. Jensen, A parabolic quasi-variational inequality arising in hydraulics. Ann. Scuola Norm. Sup. Pisa 2 (4), 421–468 (1975).Google Scholar
  11. 11.
    Ladyzhenskaja, O.A., V.A. Solonnikov & N.N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23. Amer. Math. Soc., Providence, R.I., 1968.Google Scholar
  12. 12.
    Li-Shang, C., The two phase Stefan problem II. Chinese Math.-Acta 5, 35–53 (1964) [Acta Math. Sinica 14, 33–49 (1964)].Google Scholar
  13. 13.
    Li-Shang, C., Existence and differentiability of the solution of the two-phase Stefan problem for quasi-linear parabolic equations. Chinese Math.-Acta 7, 481–496 (1965).Google Scholar
  14. 14.
    Rubinstein, L.I., Two-phase Stefan problem on a segment with one-phase initial state of thermoconductive medium. Vien. Zap. Lat. Gos. Univ. Stucki, 58, 111–148 (1964).Google Scholar
  15. 15.
    Rubinstein, L.I., The Stefan Problem. Zvaigznye, Riga, 1967.Google Scholar
  16. 16.
    Schaeffer, D.G., A new proof of the infinite differentiability of the free boundary in the Stefan problem. To appear.Google Scholar
  17. 17.
    van Moerbeke, P., An optimal stepping problem for linear reward. Acta Math. 132, 1–41 (1974).Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanston

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