Publications

(2025). The Lax-Friedrichs method in one-dimensional hemodynamics. Preprint.

Preprint arXiv

(2024). A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid. Preprint.

Preprint arXiv

(2024). Influx ratio preserving coupling conditions for the networked Lighthill-Whitham-Richards model. Proceeding in Applied Mathematics and Mechanics.

PDF DOI 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. Journal of Scientific Computing.

PDF DOI arXiv

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

PDF DOI arXiv

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

Preprint PDF DOI arXiv

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

PDF DOI arXiv

(2023). A central scheme for two 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.

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

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

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(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.

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(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.

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(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.).

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(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

SPP2410 Statusseminar 2025
Mar 10, 2025 Darmstadt, Germany
Event
Workshop in the honor of Mark Chaplain's birthday
Nov 28, 2024 St Andrews, Scotland invited
Event
Applied Mathematics Seminar (University of St Andrews)
Nov 22, 2024 St Andrews, Scotland invited
Event
Workshop SPP-2410: Nonlocal Modelling in Fluidmechanical Applications
Sep 3, 2024 Mannheim, Germany invited
13th European Conference on Mathematical and Theoretical Biology (ECMTB)
Jul 24, 2024 Toledo, Spain mini-symposium & talk
Event
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