Comptes Rendus
no. 4
Homogenization and concentrated capacity in reticular almost disconnected structures
[Homogénéisation et capacité concentrée dans les structures réticulaires presque déconnectées]
Daniele Andreucci1 ; Paolo Bisegna2 ; Emmanuele DiBenedetto3
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, Volume 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
Daniele Andreucci 1 ; Paolo Bisegna 2 ; Emmanuele DiBenedetto 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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     author = {Daniele Andreucci and Paolo Bisegna and Emmanuele DiBenedetto},
     title = {Homogenization and concentrated capacity in reticular almost disconnected structures},
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     pages = {329--332},
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     doi = {10.1016/S1631-073X(02)02482-2},
     language = {en},
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Daniele Andreucci; Paolo Bisegna; Emmanuele DiBenedetto. Homogenization and concentrated capacity in reticular almost disconnected structures. Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 329-332. doi : 10.1016/S1631-073X(02)02482-2. https://comptes-rendus.academie-sciences.fr/mathematique/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] Ph.G. Ciarlet; V. Lods Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations, Arch. Rational Mech. Anal., Volume 136 (1996), pp. 119-161

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

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

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

[7] E. Magenes 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] E.N. Pugh; T.D. Lamb 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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