The optimal shape of a dendrite sealed at both ends

Yannick Privat

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 6, page 2317-2333
  • ISSN: 0294-1449

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Privat, Yannick. "The optimal shape of a dendrite sealed at both ends." Annales de l'I.H.P. Analyse non linéaire 26.6 (2009): 2317-2333. <http://eudml.org/doc/78935>.

@article{Privat2009,
author = {Privat, Yannick},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {optimal shape; cable equation; dendrite; eigenvalue problem},
language = {eng},
number = {6},
pages = {2317-2333},
publisher = {Elsevier},
title = {The optimal shape of a dendrite sealed at both ends},
url = {http://eudml.org/doc/78935},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Privat, Yannick
TI - The optimal shape of a dendrite sealed at both ends
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2317
EP - 2333
LA - eng
KW - optimal shape; cable equation; dendrite; eigenvalue problem
UR - http://eudml.org/doc/78935
ER -

References

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  1. [1] Bandle C., Extremal problems for eigenvalues of the Sturm–Liouville type, in: General Inequalities, 5, Oberwolfach, 1986, Internat. Schriftenreibe Numer. Math., vol. 80, Birkhäuser, Basel, 1987. Zbl0638.34019MR1018157
  2. [2] Cox S.J., Lipton R., Extremal eigenvalue problems for two-phase conductors, Arch. Ration. Mech. Anal.136 (1996) 101-117. Zbl0914.49011MR1423004
  3. [3] Cox S.J., Raol J.H., Recovering the passive properties of tapered dendrites from single and dual potential recordings, Math. Biosci.190 (1) (2004) 9-37. Zbl1049.92007MR2067825
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  7. [7] Henrot A., Extremum Problems for Eigenvalues of Elliptic Operators, Front. Math., Birkhäuser, 2006. Zbl1109.35081MR2251558
  8. [8] Henrot A., Privat Y., Shape minimisation of dendritic attenuation, Appl. Math. Optim.57 (1) (February 2008) 1-16. Zbl1133.92003MR2373003
  9. [9] Henrot A., Pierre M., Variation et Optimisation de Formes, Math. Appl., Springer-Verlag, 2005. Zbl1098.49001MR2512810
  10. [10] Tosio Kato X., Perturbation Theory for Linear Operators, Classics Math., Springer-Verlag, Berlin, 1995, reprint of the 1980 edition. Zbl0836.47009MR1335452
  11. [11] Mauroy B., Filoche M., Weibel E.R., Sapoval B., An optimal bronchial tree may be dangerous, Nature427 (2004) 633-636. 
  12. [12] Mauroy B., Filoche M., Andrade J.S., Sapoval B., Interplay between geometry and flow distribution in an airway tree, Phys. Rev. Lett.90 (2003) 148101-1-148101-4. 
  13. [13] Rall W., An historical perspective on modeling dendrites, in: Stuart G., Spruston N., Häusser M. (Eds.), Dendrites, 2nd edition, Oxford University Press, 2008, Chapter 12. 
  14. [14] Rall W., Agmon-Snir H., Cable theory for dendritic neurons, in: Koch C., Segev I. (Eds.), Methods in Neuronal Modeling. From Ions to Networks, 2nd edition, MIT Press, Cambridge, MA, 1998, pp. 27-92, Chapter 2. 
  15. [15] Rall W., Theory of physiological properties of dendrites, Ann. New York Acad. Sci.96 (1962) 1071. 
  16. [16] Sokolowski J., Zolesio J.P., Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer Ser. Comput. Math., vol. 10, Springer, Berlin, 1992. Zbl0761.73003MR1215733
  17. [17] Walter J., Regular eigenvalue problem with eigenvalue parameter in the boundary condition, Math. Z.133 (1973) 301-312. Zbl0246.47058MR335935

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