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Meyer’s Topology and Brownian motion in a composite medium

  • Weian Zheng
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1626)

1991 Mathematical Subject Classification

Primary 60J65 secondary 60J60 60J35 58G32 58G11 

Résumé

On associe au problème de propagation de la chaleur dans un milieu composite un processus de diffusion qui est une semimartingale. On étudie surtout le problème de Stefan.

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References

  1. [1]
    M.Biroli and U.Mosco, “Dirichlet forms and structural estimates in discontinuous media,”, C.R.Acad.Sci.Paris, t. 313, Sery I, (1991)Google Scholar
  2. [2]
    M.Biroli and U.Mosco, “Discontinuous media and Dirichlet forms of diffusion type”, Developments in Partial Differential Equations and Applications to Math. Physics, Plenum Press, New York, (1992)Google Scholar
  3. [3]
    Z.Chen, “On reflecting diffusion processes and Skorohod decompositions”, Prob. Theory and Related Fields, Vol.94, No. 3, (1993), 281–315CrossRefzbMATHGoogle Scholar
  4. [4]
    Z.Chen, P.Fitzsimmons and R.Williams, “Reflecting Brownian motions: quasimartingales and strong caccioppoli sets”, Potential Analysis 2 (1993), p.219–243MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    C.M.Elliott and H.R.Ockendon, Weak and Variational Methods for Moving Boundary Problems, Pitman Publishing Inc. (1982)Google Scholar
  6. [6]
    M.Fukushima, Dirichlet forms and Markov Processes, North-Holland, (1985)Google Scholar
  7. [7]
    L.C.Evans and R.F.Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, (1992)Google Scholar
  8. [8]
    T.Funaki, “A certain class of diffusion processes associated with nonlinear parabolic equations,” Z.Wahrsch. verw. Gebiete, 67, (1984)Google Scholar
  9. [9]
    J.M.Hill and J.N.Dewynne, Heat Conduction, Blackwell Scientific Publications, (1987)Google Scholar
  10. [10]
    T.G.Kurtz, “Random time changes and convergence in distribution under the Meyer-Zheng conditions”, The Annals of Prob., (1991), V19, No.3, 1010–1034MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    O.A.Ladyzenskaya, V.A.Solonnikov and N.N.Uralceva, Linear and Quasilinear Equations of Parabolic Type, AMS, (1968)Google Scholar
  12. [12]
    A.V.Luikov, Analytical Heat Diffusion Theory, Academic Press, (1968)Google Scholar
  13. [13]
    T.Lyons and T.S.Zhang, “Note on convergence of Dirichlet processes”, Bull. London Math. Soc. 25 (1993), 353–356MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    T.Lyons and W.Zheng, “A Crossing estimate for the canonical process on a Dirichlet space and a tightness result”, Colloque Paul Levy sur les Processus Stochastiques, Asterisque 157–158 (1988), 249–271MathSciNetzbMATHGoogle Scholar
  15. [15]
    T.Lyons and W.Zheng, “Diffusion Processes with Non-smooth Diffusion Coefficients and Their Density Functions”, the Proceedings of Edinburgh Mathematical Society, (1990), 231–242Google Scholar
  16. [16]
    P.A.Meyer and W.Zheng, “Tightness criteria for laws of semimartingales”, Ann. Inst. Henri Poincaré. 20 (1984), No. 4, 357–372MathSciNetzbMATHGoogle Scholar
  17. [17]
    M.N,Özisik, Heat Conduction, 2nd ed., John Wiley & Sons, Inc. (1993)Google Scholar
  18. [18]
    J.Nash, “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., (1958), 80, 931–954MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M.Takeda, “Tightness property for symmetric diffusion processes” Proc. Japan Acad. Ser. A, Math. Sci., (1988), 64Google Scholar
  20. [20]
    T.Uemura, “On weak convergence of diffusion processes generated by energy forms”, Preprint, 1994Google Scholar
  21. [21]
    R.J.Williams and W.A.Zheng, “On reflecting Brownian motion—a weak convergence approach”, A. Inst. H. Poincare, (1990), 26, No.3, p.461–488MathSciNetzbMATHGoogle Scholar
  22. [22]
    W.Zheng, “Tightness results for laws of diffusion processes application to stochastic machanics”, A. Inst. H. Poincare, (1985), 21Google Scholar
  23. [23]
    W.Zheng, “Conditional propagation of chaos and a class of quasi-linear PDE”, Annals of Probobability, (1965), Vol.23, No.3, 1389–1413.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Weian Zheng
    • 1
  1. 1.Department of mathematicsUniversity of CaliforniaIrvineUSA

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