Mathematical analysis of a model of morphogenesis

Discrete and Continuous Dynamical Systems

Volumn 25, Issue 1, 2009, Pages 343-361

  Tello, J Ignacio ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Morphogens; Reaction diffusion equations; Stability of solutions. the author is supported by project dges (spain) mtm 2005 03463

Indexed keywords

EID: 70349847386     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2009.25.343     Document Type: Article

References (17)

1. R. A. Adams, "Sobolev Spaces, " Academic Press, Orlando 1975.
2. E. V. Entchev, A. Schwabedissen and M. González-Gaitán, Gradient formation of the TGF homolog DPP, Cell, 103 (2000), 981-991.
3. E. V. Entchev and M. González-Gaitán, Morphogen gradient formation and vesicular trafficking, Traffic, 3 (2002) 98-109.
4. (Pubitemid 28181621)M. Kerszberg and L. Wolpert, Mechanism for positional signalling by morphogen transport: A theoretical study, J. Theor. Biol., 191 (1998), 103-114.
5. P. Krzyzanowski, P. Laurençot and D. Wrzosek, Well-posedness and convergence to the steady state for a model of morphogen transport, SIAM J. Math. Anal., 40 (2008), 1725-1749.
6. (Pubitemid 34650074)A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion? Dev. Cell, 2 (2002), 785-796.
7. A. D. Lander, Q. Nie and F. Y. M. Wan, Internalization and end flux in morphogen gradient degradation, J. Comput. Appl. Math., 190 (2006), 232-251.
8. A. D. Lander, Q. Nie, B. Vargas and F. Y. M. Wan, Agregation of a distributed source morphogen gradient degradation, Studies in Appl. Math., 114 (2005), 343-374.
9. J. L. Lions, "Quelques Méhodes de Résolution des Problèmes aux Limites Non Linéaires, " Dunod, Paris 1969.
10. Y. Lou, Q. Nie and F. Y. M. Wan, Effects of sog DPP-Receptor binding, SIAM J. Appl. Math., 65 (2005), 343-374.
11. A. Friedman, "Partial Differential Equations of Parabolic Type, " Prentice-Hall, Englewood Cliffs, NJ, 1964.
12. D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order, " Springer, Berlin-New York, 1977.
13. J. H. Merking, D. J. Needham and B. D. Sleeman, A mathematical model for the spread of morphogens with density dependent chemosensitivity, Nonlinearity, 18 (2005), 2745-2773.
14. J. H. Merking and B. D. Sleeman, On the spread of morphogens, J. Math. Biol., 51 (2005), 1-17.
15. R. E. Showalter, "Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations, " Mathematical Surveys and Monographs. Vol 49, AMS. Providence, Rhode Island 1997.
16. A. Teleman and S. Cohen, DPP gradient formation in the Drosophila wing imaginal disc, Cell, 103 (2000), 971-980.
17. L. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. Theore. Biol., 25 (1969), 1-47.