Open Access
Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
---|---|---|
Page(s) | 419 - 448 | |
DOI | https://doi.org/10.1051/m2an/2024005 | |
Published online | 08 January 2025 |
- T. Alazard, M. Magliocca and N. Meunier, Mathematical study of a coupled incompressible darcy’s free boundary problem with surface tension. submitted. [Google Scholar]
- T. Alazard, N. Meunier and D. Smets, Lyapunov functions, identities and the cauchy problem for the hele–shaw equation. Commun. Math. Phys. 377 (2020) 1421–1459. [CrossRef] [Google Scholar]
- L. Berlyand, J. Fuhrmann and V. Rybalko, Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility. Commun. Math. Sci. 16 (2018) 735–762. [CrossRef] [MathSciNet] [Google Scholar]
- C. Blanch-Mercader and J. Casademunt, Spontaneous motility of actin lamellar fragments. Phys. Rev. Lett. 110 (2013) 078102. [CrossRef] [PubMed] [Google Scholar]
- A. Chambolle, V. Caselles, D. Cremers, M. Novaga and T. Pock, An introduction to total variation for image analysis. Theor. Found. Numer. Methods Sparse Recov. 9 (2010) 227. [Google Scholar]
- A. Cucchi, A. Mellet and N. Meunier, A Cahn-Hilliard model for cell motility. SIAM J. Math. Anal. 52 (2020) 3843–3880. [CrossRef] [MathSciNet] [Google Scholar]
- A. Cucchi, A. Mellet and N. Meunier, Self polarization and traveling wave in a model for cell crawling migration. Discrete Contin. Dyn. Syst. 42 (2022) 2381–2407. [CrossRef] [MathSciNet] [Google Scholar]
- M.C. Dallaston, Mathematical models of bubble evolution in a Hele-Shaw Cell, Ph.D. thesis, Queensland University of Technology (2013). [Google Scholar]
- O. Gallinato, M. Ohta, C. Poignard and T. Suzuki, Free boundary problem for cell protrusion formations: theoretical and numerical aspects. J. Math. Biol. 75 (2017) 263–307. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- L. Giacomelli and F. Otto, Variatonal formulation for the lubrication approximation of the hele-shaw flow. Calc. Var. Partial Differ. Equ. 13 (2001) 377–403. [CrossRef] [Google Scholar]
- V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes theory and algorithms. Springer series in computational mathematics. Springer, Berlin (1986). [CrossRef] [Google Scholar]
- F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
- C.W. Hirt and B.D. Nichols, Volume of fluid (vof) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201–225. [CrossRef] [Google Scholar]
- R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the fokker–planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [CrossRef] [MathSciNet] [Google Scholar]
- I. Lavi, N. Meunier and P. Olivier, Implicit time discretization for coupled one-phase hele-shaw problem with surface tension (in preparation). [Google Scholar]
- I. Lavi, N. Meunier, R. Voituriez and J. Casademunt, Motility and morphodynamics of confined cells. Phys. Rev. E 101 (2020) 022404. [CrossRef] [PubMed] [Google Scholar]
- F. Otto, Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory. Arch. Ration. Mech. Anal. 141 (1998) 63–103. [Google Scholar]
- C.S. Peskin, The immersed boundary method. Acta Numer. 11 (2002) 479–517. [CrossRef] [MathSciNet] [Google Scholar]
- V. Rybalko and L. Berlyand, Emergence of traveling waves and their stability in a free boundary model of cell motility. Trans. Amer. Math. Soc. 376 (2023) 1799–1844. [Google Scholar]
- F. Ziebert and I.S. Aranson, Computational approaches to substrate-based cell motility. Npj Comput. Mater. 2 (2016) 1–16. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.