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Some remarks on the homogenization of the dam problem

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Abstract

The homogenization of the dam problem is discussed in the general weak formulation by means of the technique of correctors. In the two special cases of horizontal layers and of the isotropic coefficients with separated variables the problem is solved. However, in general, the unsaturated region is not stable for the homogenization, as a counterexample by Alt shows.

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References

  1. ALT H.W. - “Strömungen durch inhomogene poröse Medien mit freien Rand”, J. für die reine und angewandte Mathematik, 305 (1979), 89–115

    Google Scholar 

  2. ALT H.W. - Oral Communication, Bonn, June (1982)

  3. ALT H.W. & L. CAFFARELLI - To appear

  4. ALT H.W. &G. GILARDI - “The behavior of the free boundary for the dam problem” Ann. Scuola Norm.Sup.Pisa9 (1981) 571–626

    Google Scholar 

  5. BAIOCCHI C. - “Su un problema a frontiera libera connesso a questioni di idraulica”. Annali Mat. Pura Appl.92 (1972), 107–127

    Google Scholar 

  6. BENCI V. - “On a filtration problem through a porous medium”, Annali Mat. Pura Appl.100 (1974), 191–209

    Google Scholar 

  7. BENSOUSSAN A. -J.L. LIONS &G. PAPANICOLAOU - “Asyniptotic Analysis for Periodic Strutures”, North-Holland, Amsterdam (1978)

    Google Scholar 

  8. BRÉZIS H. -D. KINDERLEHRER & STAMPACCHIA G. - “Sur une nouvelle formulation du problème de L'écoulement à travers une digne”, C.R.A.S. Paris287-A (1978), 711–714

    Google Scholar 

  9. CARRILLO J. &M. CHIPOT - “On the dam problem” J.Diff. Equations,45 (1982), 234–271

    Google Scholar 

  10. CODEGONE M. &J.F. RODRIGUES - “On the homogenization of the rectangular dam problem”, Rendiconti Sem. Mat. Univ. Pol. Torino,39 n.2 (1981), 125–136

    Google Scholar 

  11. De GIQRGI E. &S. SPAGNOLO - “Sulla convergenze degli integrali dell'energia per operatori elliptici del 2a. ordine”. Boll. U.M.I. (4)8 (1973), 391–411

    Google Scholar 

  12. MARINO A. &S. SPAGNOLO - “Un tipo di approssimazione dell'operatore ∑ij Di(aijDj) con operatori ∑jDi(ß(x)Dj)”, Ann. Scuol. Norm. Sup Pisa (III)23 (1969), 657–673

    Google Scholar 

  13. MURAT F. - “H-Convergence”, Seminaire d'Anal. Fonct. et Num. 1977/78, Universitē d'Alger

  14. SPAGNOLO S. - “Sulla convergence di soluzioni di equazioni paraboliche ed ellittiche” Ann. Scuola Norm. Sup. Pisa (III)22 (1968), 571–597

    Google Scholar 

  15. STAMPACCHIA G. - “Problem al contorno ellittici con datti discontinui dotati di soluzioni hölderiane”, Annali Mat. Pura Appl.51 (1960), 1–32

    Google Scholar 

  16. TARTAR L. Cours Peccot, College de France, Paris, 1977 (see also [M] and Proc. of the Japan-France Seminar 1976, Ed. by H. Fugita, Japan Soc. for Promotion of Science (1978), p. 469–482)

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  1. Centro de Matemātica e Aplicações Fundamentais, Av. Prof. Gama Pinto, 2, 1699, Lisboa codex, Portugal

    José-francisco Rodrigues

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  1. José-francisco Rodrigues
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Rodrigues, Jf. Some remarks on the homogenization of the dam problem. Manuscripta Math 46, 65–82 (1984). https://doi.org/10.1007/BF01185195

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