Publications

(2024). Influx ratio preserving coupling conditions for the networked Lighthill-Whitham-Richards model. Submitted.

Preprint arXiv

(2024). A one-dimensional model for aspiration therapy in blood vessels. Preprint.

Preprint arXiv

(2024). Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation. Submitted.

Preprint arXiv

(2023). Numerical schemes for coupled systems of nonconservative hyperbolic equations. Accepted in SIAM Journal on Numerical Analysis.

Preprint arXiv

(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. Communications on Applied Mathematics and Computation.

PDF DOI arXiv

(2022). Data-Driven Models for Traffic Flow at Junctions. Mathematical Methods in the Applied Sciences.

PDF DOI 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.

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

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

PDF 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

European Congress of Mathematics (ECM) 2024
Jul 16, 2024 Seville, Spain invited
Webinar of the DFG SPP 2410 CoScaRa
Jun 11, 2024 Online
3rd International workshop on Perspectives on Multiphase Fluid Dynamics, Continuum Mechanics and Hyperbolic Balance Laws (ProHyp2024)
Apr 25, 2024 Trento, Italy
Event
94th Annual Meeting of the Association of Applied Mathematics and Mechanics (GAMM)
Mar 20, 2024 Magdeburg, Germany
Workshop on Mathematical modeling, Analysis and Approximation of Vehicular and Pedestrian Dynamics
Jun 6, 2023 Tours, France 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