no. 4
Homogenization and concentrated capacity in reticular almost disconnected structures
[Homogénéisation et capacité concentrée dans les structures réticulaires presque déconnectées]
Andreucci, Daniele1 ; Bisegna, Paolo2 ; DiBenedetto, Emmanuele3
1 Dipartimento di Metodi e Modelli, Università di Roma La Sapienza, via A. Scarpa 16, 00161 Rome, Italy
2 Dipartimento di Ingegneria Civile, Università di Roma Tor Vergata, 00133 Rome, Italy
3 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 329-332.

On calcule la limite homogénéisée-concentrée pour deux équations de diffusion couplées de façon non linéaire dans un domaine cylindrique avec une distribution périodique de cavités cylindriques coaxiales le long de son axe. Ce problème émane de la transduction visuelle.

We compute the homogenized-concentrated limit for a pair of non-linearly coupled diffusion equations in a perforated cylindric domain with coaxial cylindric holes periodically distributed along its axis. This problem arises from visual transduction.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02482-2
Andreucci, Daniele 1 ; Bisegna, Paolo 2 ; DiBenedetto, Emmanuele 3

1 Dipartimento di Metodi e Modelli, Università di Roma La Sapienza, via A. Scarpa 16, 00161 Rome, Italy
2 Dipartimento di Ingegneria Civile, Università di Roma Tor Vergata, 00133 Rome, Italy
3 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA 
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     title = {Homogenization and concentrated capacity in reticular almost disconnected structures},
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     pages = {329--332},
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Andreucci, Daniele; Bisegna, Paolo; DiBenedetto, Emmanuele. Homogenization and concentrated capacity in reticular almost disconnected structures. Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 329-332. doi : 10.1016/S1631-073X(02)02482-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02482-2/

[1] D. Andreucci, P. Bisegna, E. DiBenedetto, H.H. Hamm, Mathematical models of the dynamics of the second messengers in visual transduction: Homogenization and concentrated capacity, Preprint, 2002

[2] D. Andreucci, P. Bisegna, E. DiBenedetto, Homogenization and concentrated capacity limits for a problem in visual transduction, Preprint, 2002

[3] Ciarlet, Ph.G.; Lods, V. Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations, Arch. Rational Mech. Anal., Volume 136 (1996), pp. 119-161

[4] Cioranescu, D.; Saint Jean Paulin, J. Homogenization of Reticulated Structures, Appl. Math. Sci., 136, Springer, New York, NY, 1998

[5] Colli, P.; Rodrigues, J.F. Diffusion through thin layers with high specific heat, Asymptotic Anal., Volume 3 (1990), pp. 249-263

[6] DiBenedetto, E. Real Analysis, Birkhäuser, Boston, 2002

[7] Magenes, E. Stefan problems with a concentrated capacity, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), Volume 1 (1998) no. 1, pp. 71-81

[8] Pugh, E.N.; Lamb, T.D. Phototransduction in vertebrate rods and cones: Molecular mechanisms of amplification, recovery and light adaptation, Handbook of Biological Physics, 3, Elsevier, 2000 (Chapter 5)

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