Numerical Preservation of Velocity Induced Invariant Regions for Reaction–Diffusion Systems on Evolving Surfaces
暂无分享,去创建一个
Anotida Madzvamuse | Chandrasekhar Venkataraman | Ivonne Sgura | Massimo Frittelli | C. Venkataraman | A. Madzvamuse | I. Sgura | Massimo Frittelli
[1] Anotida Madzvamuse,et al. Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces , 2017, Comput. Math. Appl..
[2] C. M. Elliott,et al. Modelling cell motility and chemotaxis with evolving surface finite elements , 2012, Journal of The Royal Society Interface.
[3] R. A. Barrio,et al. The Effect of Growth and Curvature on Pattern Formation , 2004 .
[4] G. M.,et al. Partial Differential Equations I , 2023, Applied Mathematical Sciences.
[5] J. Smoller. Shock Waves and Reaction-Diffusion Equations , 1983 .
[6] Sabine Fenstermacher,et al. Numerical Approximation Of Partial Differential Equations , 2016 .
[7] Anotida Madzvamuse,et al. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains , 2010, Journal of mathematical biology.
[8] Emmanuel Hebey. Sobolev spaces on manifolds , 2008 .
[9] N. Tuncer,et al. Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces , 2017 .
[10] Buyang Li,et al. Convergence of finite elements on an evolving surface driven by diffusion on the surface , 2016, Numerische Mathematik.
[11] Richard Tsai,et al. An implicit boundary integral method for computing electric potential of macromolecules in solvent , 2017, J. Comput. Phys..
[12] Grady B. Wright,et al. A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces , 2012, Journal of Scientific Computing.
[13] D. Lacitignola,et al. Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay , 2014, European Journal of Applied Mathematics.
[14] P. Maini,et al. Reaction and diffusion on growing domains: Scenarios for robust pattern formation , 1999, Bulletin of mathematical biology.
[15] Ivonne Sgura,et al. Virtual Element Method for the Laplace-Beltrami equation on surfaces , 2016, 1612.02369.
[16] Charles M. Elliott,et al. L2-estimates for the evolving surface finite element method , 2012, Math. Comput..
[17] A. Madzvamuse,et al. Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.
[18] Anotida Madzvamuse,et al. Preserving invariance properties of reaction–diffusion systems on stationary surfaces , 2016, 1609.02741.
[19] O. Lakkis,et al. Global existence for semilinear reaction–diffusion systems on evolving domains , 2010, Journal of Mathematical Biology.
[20] Constantino Carlos Reyes-Aldasoro,et al. Whole cell tracking through the optimal control of geometric evolution laws , 2015, J. Comput. Phys..
[21] Guillermo Sapiro,et al. Variational Problems and Partial Differential Equations on Implicit Surfaces: Bye Bye Triangulated Surfaces? , 2003 .
[22] J. Schnakenberg,et al. Simple chemical reaction systems with limit cycle behaviour. , 1979, Journal of theoretical biology.
[23] A. Bretscher,et al. Polarization of cell growth in yeast. , 2000, Journal of cell science.
[24] Chieh Chen,et al. An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics , 2015, 1604.00285.
[25] C. M. Elliott,et al. Error analysis for an ALE evolving surface finite element method , 2014, 1403.1402.
[26] Jean-Francois Mangin,et al. A Reaction-Diffusion Model of Human Brain Development , 2010, PLoS computational biology.
[27] F. Yang,et al. A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws , 2016, 1603.08572.
[28] S. Bhat,et al. Modeling and analysis of mass-action kinetics , 2009, IEEE Control Systems.
[29] Y. Couder,et al. Turning a plant tissue into a living cell froth through isotropic growth , 2009, Proceedings of the National Academy of Sciences.
[30] A. Quarteroni,et al. Numerical Approximation of Partial Differential Equations , 2008 .
[31] Charles M. Elliott,et al. Finite element methods for surface PDEs* , 2013, Acta Numerica.
[32] Charles M. Elliott,et al. Finite elements on evolving surfaces , 2007 .
[33] B. Kovács,et al. Computing arbitrary Lagrangian Eulerian maps for evolving surfaces , 2016, Numerical Methods for Partial Differential Equations.
[34] S. I. Hariharan,et al. Numerical methods for partial differential equations , 1986 .
[35] Zhenbiao Yang,et al. Control of Pollen Tube Tip Growth by a Rop GTPase–Dependent Pathway That Leads to Tip-Localized Calcium Influx , 1999, Plant Cell.
[36] N. Rashevsky,et al. Mathematical biology , 1961, Connecticut medicine.
[37] Michael E. Taylor,et al. Partial Differential Equations III , 1996 .
[38] Deborah Lacitignola,et al. Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition , 2017, Commun. Nonlinear Sci. Numer. Simul..
[39] Andrew J. Wathen,et al. A moving grid finite element method applied to a model biological pattern generator , 2003 .
[40] C. M. Elliott,et al. The surface finite element method for pattern formation on evolving biological surfaces , 2011, Journal of mathematical biology.
[41] Arnold Reusken,et al. A Higher Order Finite Element Method for Partial Differential Equations on Surfaces , 2016, SIAM J. Numer. Anal..
[42] Patrik Sahlin,et al. A Modeling Study on How Cell Division Affects Properties of Epithelial Tissues Under Isotropic Growth , 2010, PloS one.
[43] A. Bretscher,et al. Polarization of cell growth in yeast. I. Establishment and maintenance of polarity states. , 2000, Journal of cell science.
[44] Li-Tien Cheng,et al. Variational Problems and Partial Differential Equations on Implicit Surfaces: The Framework and Exam , 2000 .
[45] Rodrigo Ramos-Jiliberto,et al. Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability , 2003 .