On a nonlinear flux-limited equation arising in the transport of morphogens

Motivated by a mathematical model for the transport of morphogens in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial–boundary value problem associated with a nonlinear flux-limited diffusion system. From a mathematical point of view the problem behaves...

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Bibliographic Details
Published in:Journal of Differential Equations 2012-05, Vol.252 (10), p.5763-5813
Main Authors: Andreu, F., Calvo, J., Mazón, J.M., Soler, J.
Format: Article
Language:English
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Summary:Motivated by a mathematical model for the transport of morphogens in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial–boundary value problem associated with a nonlinear flux-limited diffusion system. From a mathematical point of view the problem behaves more as a hyperbolic system than a parabolic one.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.01.017