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Partial Differential Equations in China pp 67–79Cite as

Free Boundary Problems

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 288))

Abstract

The study of the free boundary problems was started working in China as early as 1960 ([14] [19]). Since then many mathematicians have been concentrating their effects to the theoretical researches on phase change problems, filtration problems, etc.

1991 Mathematics Subject Classification: 35R35

Supported by NNSF of China

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References

  1. Chang K.C., The obstacle problem and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. Vol.33 (1980), 117–146.

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang K.C., Free boundary problems and the set-valued mappings, J.D.E. Vol.49 (1983), No. 1, 1–28.

    Article  MATH  Google Scholar 

  3. Chang K.C. and Jiang B.J., Fixed point index of the set-valued mappings and multiplicity of solutions of elliptic equations with discontinuous nonlinearities, Acta Math. Sinica, Vol. 21 (1978), 26–43.

    MathSciNet  Google Scholar 

  4. Chang K.C. and Jiang L.S., The free boundary problem of the stationary water cone, Acta Sci. Natur. Univ. Peking (1978) 1–25.

    Google Scholar 

  5. Cryer C.W. and Zhou S.Z., The solution of the free boundary problem for an axisymmetric partially penetrating well, Annali Mat. Pure Appl. Ser. 4, Vol.85 (1983), 219–236.

    Article  MathSciNet  Google Scholar 

  6. Friedman A. and Jiang L.S., A Stefan-Signorini problem, J. Diff. Equ., Vol.51 (1984), 213–231.

    Article  MathSciNet  MATH  Google Scholar 

  7. Gu L.K., The behavior of the solution for the Stefan problem as time increase infinitely, Dokl. Akad. Nauk SSSR, Vol. 138 (1961), 263–266.

    MathSciNet  Google Scholar 

  8. Gu L.K., The asymptotic behavior of the solution of the multi-phase Stefan problem, Acta Math. Sinica, Vol.23 (1980), 203–214.

    MathSciNet  MATH  Google Scholar 

  9. Han H.T., The two-phase Stefan problem for quasilinear parabolic equations, Collection of papers on diff. equ., Peking Univ., (1963), 57–65.

    Google Scholar 

  10. Huang S.Y., A free boundary problem connected with non-steady porous flow well, Acta Math. Sinica, Vol.25 (1982), 754–768.

    MathSciNet  MATH  Google Scholar 

  11. Huang S.Y., The free boundary problem for a partially penetrating well, Acta Math. Sinica, Vol.28 (1985), 71–84.

    MathSciNet  MATH  Google Scholar 

  12. Huang S.Y and Wang Y.D., A free boundary problem in an unbounded domain Acta Math. Sinica, Vol. 26 (1983), 354–377.

    MathSciNet  MATH  Google Scholar 

  13. Huang S.Y. and Wang Y.D., The free boundary problem of the stationary water cone and its numerical approximation, Acta Sci. Natur. Peking Univ., (1983), 1–25.

    Google Scholar 

  14. Jiang L.S., The free boundary problem for nonlinear parabolic equations, Acta Math. Sinica, Vol. 5 (1962), 208–223.

    Google Scholar 

  15. Jiang L.S., Correctness of a free boundary problem for nonlinear parabolic equations, Acta Math. Sinica, Vol.12 (1962), 369–388; translated as Chinese Math. Acta, Vol. 3 (1963), 399-418.

    MATH  Google Scholar 

  16. Jiang L.S., Two phase Stefan problem (I), Acta Math. Sinica, Vol. 13 (1963), 631–646; translated as Chinese Math. Acta, Vol.4(l964), 686-702.

    MATH  Google Scholar 

  17. Jiang L.S., Two-phase Stefan problem (II), Acta Math. Sinica, Vol.14 (1964), 33–49; translated as Chinese Math. Acta, Vol.5 (1964), 36-53.

    MATH  Google Scholar 

  18. Jiang L.S., Existence and differentiability of the solution of the two-phase Stefan problem for quasilinear parabolic equations, Acta Math. Sinica, Vol. 15 (1965), 749–764; translated as Chinese Math. Acta, Vol. 7 (1965), 481-496.

    Google Scholar 

  19. Jiang L.S., Free boundary problems in China, Numerical Treatment of Free Boundary Value Problems, J. Albrecht, L. Collatz, K. H. Hoffman, (Eds), Birhhauser Verlag, Basel (1982), 176–186.

    Google Scholar 

  20. Jiang L.S., Remarks on the Stefan-Signorini peoblem, Free Boundary Problems: Applications & Theory (III), A Bossavit, A. Damlamian, M. Premond, (Eds), Research Notes in Math. (120) Pitman (1985), 13–19.

    Google Scholar 

  21. Jiang L.S., On an elastic-plastic problem, J. Diff. Equ., Vol.51 (1984), 97–115.

    Article  MATH  Google Scholar 

  22. Jiang L.S. and Wu L.C. etc., On the existence, uniqueness of a kind of elasticplastic problems and the convergence of the approximate solutions, Acta Math. Appl. Sinica, Vol. 4 (1981), 166–174.

    MathSciNet  MATH  Google Scholar 

  23. Jiang L.S. and Wu L.C., A class of nonlinear elliptic systems with discontinuous coefficients, Acta Math. Sinica, Vol.26 (1983), 660–668.

    MathSciNet  MATH  Google Scholar 

  24. Jiang L.S. and Xie W.Q., A two-phase Stefan-Signorini problem, Acta Sci. Natur. Peking Univ., (1986), 1–14.

    Google Scholar 

  25. Liu X.Y., Stefan-Signorini problem of quasilinear parabolic equations, Acta Math. Natur. Peking Univ., (1988), 19–32.

    Google Scholar 

  26. Mai M.C., Existence of the solution for two-phase Stefan problem, Collection of papers on diff. equ. Peking Univ., (1963) 45–56.

    Google Scholar 

  27. Wang Y.D. and Huang S.Y., Regularity of the solution for compressible flow well problem, Acta Math, and Phys., Vol.5 (1985), 147–166.

    Google Scholar 

  28. Yu W.H., Existence of solution for a two-phase Stefan-Signorini problem in one-dimensional case, J. Partial Diff. Equ., Vol.1, Ser. B, No.2, (1988), 67–83.

    MATH  Google Scholar 

  29. Friedman A., One dimensional Stefan problems with nonmonotone free boundary, Trans. AMS, Vol. 133 (1968), 89–114.

    Article  MATH  Google Scholar 

  30. Friedman A., Analyticity of the free boundary of Stefan problems, Arch. Rat. Mech. Anal, Vol. 61 (1976), 97–125.

    Article  MATH  Google Scholar 

  31. Kyner W.T., An existence and uniqueness theorem for a nonlinear Stefan problem, J. Math. Mech., Vol. 8 (1959), 483–498.

    MathSciNet  MATH  Google Scholar 

  32. Sestini G., Sul problema unidimensionale non lineare di Stefan in uno strato piano indefinito, Annali Mat. Pura Appl., Vol.51 (1960), 203–224.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Suzhou University, Suzhou, 215006, P.R. China

    Lishang Jiang

Authors
  1. Lishang Jiang
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Editor information

Editors and Affiliations

  1. Fudan University, Shanghai, China

    Chaohao Gu

  2. Institute of Applied Mathematics, Academia Sinica, Beijing, China

    Xiaxi Ding

  3. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Chung-Chun Yang

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© 1994 Springer Science+Business Media Dordrecht

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Jiang, L. (1994). Free Boundary Problems. In: Gu, C., Ding, X., Yang, CC. (eds) Partial Differential Equations in China. Mathematics and Its Applications, vol 288. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1198-0_6

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  • DOI: https://doi.org/10.1007/978-94-011-1198-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4524-7

  • Online ISBN: 978-94-011-1198-0

  • eBook Packages: Springer Book Archive

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