Stability estimates for systems with small cross-diffusion
| Autor: | Yves Capdeboscq, Luca Alasio, Maria Bruna |
|---|---|
| Přispěvatelé: | Gran Sasso Science Institute (GSSI), Istituto Nazionale di Fisica Nucleare (INFN), Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge [UK] (CAM), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), National Institute for Nuclear Physics (INFN), Department of Applied Mathematics and Theoretical Physics / Centre for Mathematical Sciences (DAMTP/CMS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Mathematical and theoretical biology 35K55 35B30 35Q92 65M15 Applied Mathematics 010102 general mathematics Banach space 01 natural sciences Stability (probability) 010101 applied mathematics Computational Mathematics Mathematics - Analysis of PDEs Modeling and Simulation FOS: Mathematics Applied mathematics A priori and a posteriori [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Limit (mathematics) Boundary value problem 0101 mathematics Diffusion (business) Focus (optics) Analysis [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2018, 52 (3), pp.1109--1135. ⟨10.1051/m2an/2018036⟩ |
| ISSN: | 0764-583X 1290-3841 |
| DOI: | 10.1051/m2an/2018036⟩ |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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