List of publications

Cancer Growth

• Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model, (J. Giesselmann, N. Kolbe, M. Lukacova, and N. Sfakianakis), (accepted in) Discrete Cont. Dyn.-B, arXiv:1704.08208, (2017)
• A multiscale approach to the migration of cancer stem cells : mathematical modelling and simulations, (N. Sfakianakis, N. Kolbe, N. Hellmann, and M. Lukacova), Bull. Math. Biol., 79, (2016), 209-235
• A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: the urokinase model, (N. Kolbe, J. Katuchova, N. Sfakianakis, N. Hellmann, and M. Lukacova), Appl. Math. Comput., 273, (2016), 353-376
• A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix, (N. Hellmann, N. Kolbe, and N. Sfakianakis), Bull. Braz. Math. Soc., 47(1), (2016), 1-16
• Numerical simulation of a contractivity based multiscale cancer invasion model, (N. Kolbe, M. Lukacova, N. Sfakianakis, and B. Wiebe) in Mult. Mod. in Mechano- and Tumor Biology: Modeling, Homogenization, and Applications edited by A. Gerisch, R. Penta, and J. Lang, arXiv:1605.05060, (2016)
• (in review) A flexible multidimensional rectangular mesh administration and refinement technique with application in cancer invasion models, (N. Kolbe and N. Sfakianakis), arXiv:1706.06191, (2017)

Live Cell Motility

• Chemotaxis and haptotaxis on a cellular level, (A. Brunk, N. Kolbe, and N. Sfakianakis) (accepted in) Springer P. Math. Stat., arXiv:1612.02345, (2017)
• Numerical treatment of the Filament Based Lamellipodium Model (FBLM), (A. Manhart, D. Oelz, Ch. Schmeiser, and N. Sfakianakis), in Mod. Cell. Syst. edited by F. Matthaeus, F. Graw, J. Pahle, arXiv : 1505.04266, (2016)
• An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals, (A. Manhart, D. Oelz, Ch. Schmeiser, and N. Sfakianakis), J. Theor. Biol., 382, (2015) 244-258
• Stable length distributions in co-localized polymerizing and depolymerizing protein filaments, (H. Freistuehler, Chr. Schmeiser, and N. Sfakianakis), SIAM J. Appl. Math., 72, (2012), 1428-1448
• (in review) Stability, convergence, and sensitivity analysis of the FBLM-FEM, (A. Brunk and N. Sfakianakis), arXiv:1801.09247, (2017)

Adaptive Mesh Refinement methods

• Entropy dissipation of moving mesh adaptation, (M. Lukacova and N. Sfakianakis), J. Hyperbol. Differ. Eq., 11 (2014), 633-653
• Theoretical study of entropy dissipation of moving meshes, (M. Lukacova, and N. Sfakianakis), AIMS on Appl. Math., 8, (2014), 931-94
• Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound, (N. Sfakianakis) Math. Comput., 82, (2013), 129-151
• Entropy conservative schemes and adaptive mesh selection for hyperbolic conservation laws, (Chr. Arvanitis, Ch. Makridakis, and N. Sfakianakis), J. Hyperbol. Differ. Eq., 7, (2010), 383-404
• (in review) A flexible multidimensional rectangular mesh administration and refinement technique with application in cancer invasion models, (N. Kolbe and N. Sfakianakis), arXiv:1706.06191, (2017)

Other Problems

• Energy intake functions of ectotherms and endothemrs derived from their body mass growth, (J. Werner, N. Sfakianakis, E.M. Griebeler, and A. Rendall), J. Theor. Biol. (2018), https://doi.org/10.1016/j.jtbi.2018.02.007
• Symetries and Asymetries of the Immune System: a categorification approach, (J.F. Mascari, D. Giacchero, and N. Sfakianakis), IEEE International Conference on Bioinformatics and Biomedicine (2017)
• Inverse modeling of the Drosophila gap gene system: Sparsity Promoting Bayesian parameter estimation and uncertainty quantification, (N. Sfakianakis, M. Simon), Proc. 10th Int. Comput. Systems Biology (2013), 86-91