Publications

(2023). A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model. Submitted.

Preprint arXiv

(2023). A data-driven microscopic on-ramp model based on macroscopic network flows. Submitted.

Preprint arXiv

(2023). A central scheme for coupled hyperbolic systems. Accepted in Communications on Applied Mathematics and Computation.

Preprint arXiv

(2022). Data-Driven Models for Traffic Flow at Junctions. Submitted.

Preprint arXiv Code

(2022). Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws. Proceedings in Applied Mathematics and Mechanics.

PDF DOI arXiv

(2022). Central schemes for networked scalar conservation laws. Networks and Heterogeneous Media.

PDF DOI arXiv Code

(2022). Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling. PLOS Computational Biology.

PDF DOI HTML Code

(2021). A mass-conservative Lagrange-Galerkin scheme of second order in time for convection-diffusion problems. Journal of Scientific Computing.

PDF DOI

(2021). An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models. Journal of Computational and Applied Mathematics.

Preprint DOI arXiv

(2021). Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs. Multiscale Modeling and Simulation.

PDF DOI arXiv

(2020). Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. Discrete Contin. Dyn. Syst. Ser. B.

Preprint DOI arXiv Supplementary material

(2019). A hybrid mass transport finite element method for Keller–Segel type systems. J. Sci. Comput.

PDF DOI arXiv

(2018). Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model. Discrete Contin. Dyn. Syst. Ser. B.

Preprint DOI arXiv

(2018). A tumor invasion model for heterogeneous cancer cell populations: mathematical analysis and numerical methods. PhD Thesis.

PDF DOI

(2018). Chemotaxis and Haptotaxis on Cellular Level. Theory, Numerics and Applications of Hyperbolic Problems I.

Preprint DOI arXiv

(2017). A Multiscale Approach to the Migration of Cancer Stem Cells: Mathematical Modelling and Simulations. Bull. Math. Biol.

Preprint PDF DOI arXiv

(2017). Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model. Multiscale Models in Mechano and Tumor Biology.

Preprint DOI arXiv

(2016). A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix. Bull. Braz. Math. Soc. (N.S.).

Preprint PDF DOI arXiv

(2016). A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: The urokinase model. Appl. Math. Comput.

Preprint PDF DOI arXiv

Talks

Workshop on Mathematical modeling, Analysis and Approximation of Vehicular and Pedestrian Dynamics
Jun 6, 2023 Tours, France invited
93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics
Jun 1, 2023 Dresden, Germany
BiMed-Math Seminar of the Institute for the Advanced Study of Human Biology
Apr 18, 2023 Kyoto University, Kyoto, Japan invited
Seminar of the research training group 'Energy, Entropy, and Dissipative Dynamics'
Dec 15, 2022 RWTH Aachen University, Aachen, Germany
Announcement
Seminar of the TU Kaiserslautern Numerics group
Dec 8, 2022 Technical University of Kaiserslautern, Kaiserslautern, Germany invited
See all talks

Contact

  • kolbe@igpm.rwth-aachen.de
  • Office 127.2, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany