Author
Alasio, L
Bruna, M
Capdeboscq, Y
Journal title
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
DOI
10.1051/m2an/2018036
Last updated
2019-04-26T22:26:52.857+01:00
Abstract
We discuss the analysis and stability of a family of cross-diffusion boundary
value problems with nonlinear diffusion and drift terms. We assume that these
systems are close, in a suitable sense, to a set of decoupled and linear
problems. We focus on stability estimates, that is, continuous dependence of
solutions with respect to the nonlinearities in the diffusion and in the drift
terms. We establish well-posedness and stability estimates in an appropriate
Banach space. Under additional assumptions we show that these estimates are
time independent. These results apply to several problems from mathematical
biology; they allow comparisons between the solutions of different models a
priori. For specific cell motility models from the literature, we illustrate
the limit of the stability estimates we have derived numerically, and we
document the behaviour of the solutions for extremal values of the parameters.
Symplectic ID
821081
Download URL
http://arxiv.org/abs/1801.06470v2
Publication type
Journal Article
Publication date
13 September 2018
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