Paper Info
Title
Well-Posedness and Convergence to the Steady State for a Model of Morphogen Transport
Abstract
Well-posedness and large time convergence to the unique steady state are shown for a model which describes the spreading of morphogens by a nonlinear transport mechanism ( transcytosis) and couples a quasilinear parabolic partial differential equation with an ordinary differential equation. A simpler model which assumes linear transport is also investigated for comparison. The analysis of both models requires the construction of specific Liapunov functionals. The study is supplemented by numerical simulations of the sensitivity of the models to the variation of their parameters.
Year
DOI
Venue
2008
10.1137/070711608
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
degenerate parabolic system,Liapunov functional,steady state
Convergence (routing),Parabolic partial differential equation,Mathematical optimization,Nonlinear system,Ordinary differential equation,Mathematical analysis,Linear model,Steady state,Partial differential equation,Mathematics,Parabola
Journal
Volume
Issue
ISSN
40
5
0036-1410
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Piotr Krzyzanowski1163.69
Philippe Laurençot23010.30
Dariusz Wrzosek321.24