메뉴 건너뛰기




Volumn 40, Issue 5, 2009, Pages 1725-1749

Well-posedness and convergence to the steady state for a model of morphogen transport

Author keywords

Degenerate parabolic system; Liapunov functional; Steady state

Indexed keywords

DEGENERATE PARABOLIC SYSTEM; LIAPUNOV FUNCTIONAL; LIAPUNOV FUNCTIONALS; MORPHOGENS; NONLINEAR TRANSPORT; NUMERICAL SIMULATION; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS; QUASI-LINEAR; STEADY STATE; TRANSCYTOSIS; WELLPOSEDNESS;

EID: 70349883614     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070711608     Document Type: Article
Times cited : (10)

References (11)
  • 1
    • 0040391541 scopus 로고
    • Highly degenerate quasilinear parabolic systems
    • H. Amann, Highly degenerate quasilinear parabolic systems, Ann. Scuola Norm. Sup. Pisa CI. Sci. (4), 18 (1991), pp. 135-166.
    • (1991) Ann. Scuola Norm. Sup. Pisa CI. Sci. , vol.4 , Issue.18 , pp. 135-166
    • Amann, H.1
  • 2
    • 0001056475 scopus 로고
    • 1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions
    • Ph. Bénilan, M. G. Crandall, and P. Sacks, Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim., 17 (1988), pp. 203-224.
    • (1988) Appl. Math. Optim. , vol.17 , pp. 203-224
    • Bénilan, Ph.1    Crandall, M.G.2    Sacks, P.3
  • 5
    • 0036106324 scopus 로고    scopus 로고
    • Morphogen gradient formation and vesicular trafficking
    • E. V. Entchev and M. A. González-Gaitán, Morphogen gradient formation and vesicular trafficking, Traffic, 3 (2002), pp. 98-109.
    • (2002) Traffic , vol.3 , pp. 98-109
    • Entchev, E.V.1    González-Gaitán, M.A.2
  • 6
    • 0032492436 scopus 로고    scopus 로고
    • Mechanisms for positional signalling by morphogen transport: A theoretical study
    • M. Kerszberg and L. Wolpert, Mechanisms for positional signalling by morphogen transport: A theoretical study, J. Theoret. Biol., 191 (1998), pp. 103-114.
    • (1998) J. Theoret. Biol. , vol.191 , pp. 103-114
    • Kerszberg, M.1    Wolpert, L.2
  • 8
    • 0036080430 scopus 로고    scopus 로고
    • Do morphogen gradients arise by diffusion?
    • A. D. Lander, Q. Nie, and F. Y. M. Wan, Do morphogen gradients arise by diffusion?. Dev. Cell, 2 (2002), pp. 785-796.
    • (2002) Dev. Cell , vol.2 , pp. 785-796
    • Lander, A.D.1    Nie, Q.2    Wan, F.Y.M.3
  • 9
    • 26944477352 scopus 로고    scopus 로고
    • A mathematical model for the spread of morphogens with density dependent chemosensitivity
    • J. H. Merkin, D. J. Needham, and B. D. Sleeman, A mathematical model for the spread of morphogens with density dependent chemosensitivity, Nonlinearity, 18 (2005), pp. 2745- 2773.
    • (2005) Nonlinearity , vol.18 , pp. 2745-2773
    • Merkin, J.H.1    Needham, D.J.2    Sleeman, B.D.3
  • 10
    • 0003316678 scopus 로고
    • Semigroups of linear operators and applications to partial differential equations
    • Springer-Verlag, New York
    • A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.44
    • Pazy, A.1
  • 11
    • 0036849180 scopus 로고    scopus 로고
    • Morphogen transport along epithelia, an integrated trafficking problem
    • J.-P. Vincent and L. Dubois, Morphogen transport along epithelia, an integrated trafficking problem, Dev. Cell, 3 (2002), pp. 615-623.
    • (2002) Dev. Cell , vol.3 , pp. 615-623
    • Vincent, J.-P.1    Dubois, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.