List of Publications

Published & Accepted Papers

  1. N. David, F. Santambrogio, M. Schmidtchen: Uniform regularity estimates for nonlinear diffusion–advection equations in the hard-congestion limit. Nonlinear Analysis, 263, 113953, 2026.
  2. M. Bruna, M. Schmidtchen, O. de Wit: Convergence of a finite volume scheme for a model for ants. ESAIM: M2AN, 59(6), 3301–3340, 2025.
  3. T. Dębiec, M. Mandal, M. Schmidtchen: From finite to continuous phenotypes in (visco-)elastic tissue growth models. Journal of Differential Equations, 437, 113375, 2025.
  4. R. M. Crossley, J.-F. Pietschmann, M. Schmidtchen: Existence of weak solutions for a volume-filling model of cell invasion into extracellular matrix. Journal of Differential Equations, 428, 721–746, 2025.
  5. G. Foghem, D. Padilla-Garza, M. Schmidtchen: Gradient flow solutions for porous medium equations with nonlocal Lévy-type pressure. Calculus of Variations and Partial Differential Equations, 64, 88, 2025.
  6. M. Di Francesco, V. Iorio, M. Schmidtchen: The approximation of the quadratic porous medium equation via nonlocal interacting particles subject to repulsive Morse potential. SIMA, 57(5), 4631–4679, 2025.
  7. T. Dębiec, M. Schmidtchen: Nonlocal approximation of an anisotropic cross-diffusion system. Nonlinear Analysis, 260, 113835, 2025.
  8. J. I. M. Hauser, V. Iorio, M. Schmidtchen: A convergent finite volume method for a kinetic model for interacting species. Kinetic and Related Models, 18(3), 343–367, 2025.
  9. N. David, M. Schmidtchen: On the Incompressible Limit for a Tumour Growth Model incorporating Convective Effects. CPAM, 77(5), 2613–2650, 2024.
  10. W. D. Martinson, A. Volkening, M. Schmidtchen, C. Venkataraman, J. A. Carrillo: Linking discrete and continuous models of cell birth and migration. Royal Society Open Science, 11(7), 232002, 2024.
  11. N. David, T. Dębiec, M. Mandal, M. Schmidtchen: A degenerate cross-diffusion system as the inviscid limit of a nonlocal tissue growth model. SIMA, 56(2), 2090–2114, 2024.
  12. A. Esposito, R. S. Gvalani, A. Schlichting, M. Schmidtchen: On a novel gradient flow structure for the aggregation equation. Calculus of Variations and Partial Differential Equations, 63, 126, 2024.
  13. M. Bruna, S. J. Chapman, M. Schmidtchen: Derivation of a macroscopic model for Brownian hard needles. Proc. R. Soc. A, 2023.
  14. G. Bevilacqua, B. Perthame, M. Schmidtchen: The Aronson-Bénilan Estimate in Lebesgue Spaces. Ann. Inst. H. Poincaré C, 40(2), 259–286, 2023.
  15. G. Heinze, J.-F. Pietschmann, M. Schmidtchen: Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities. SIMA, 55(6), 7039–7076, 2023.
  16. G. Heinze, J.-F. Pietschmann, M. Schmidtchen: Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics. Kinetic and Related Models, 16(6), 795–827, 2023.
  17. T. Dębiec, B. Perthame, M. Schmidtchen, N. Vauchelet: Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension. Journal de Mathématique Pures et Appliquées, 145, 204–239, 2021.
  18. M. Di Francesco, A. Esposito, M. Schmidtchen: Many-particle limit for a system of interaction equations driven by Newtonian potentials. Calculus of Variations and Partial Differential Equations, 2021.
  19. J. Crodelle, C. Vallejo, M. Schmidtchen, C. M. Topaz, M. R. D'Orsogna: Impacts of California Proposition 47 on Crime in Santa Monica, CA. PLOS ONE, 2021.
  20. T. Dębiec, M. Schmidtchen: Incompressible limit for a two-species tumour model with coupling through Brinkman’s law in one dimension. Act. Appl. Math., 2020.
  21. L. Alasio, H. Ranetbauer, M. Schmidtchen, M.-T. Wolfram: Trend to Equilibrium for Systems with Small Cross-Diffusion. M2AN, 2020.
  22. F. Bubba, B. Perthame, C. Pouchol, M. Schmidtchen: Hele-Shaw limit for a system of two reaction-(cross-)diffusion equations for living tissues. ARMA, 2020.
  23. J. A. Carrillo, M. Di Francesco, A. Esposito, S. Fagioli, M. Schmidtchen: Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions. DCDS, 2020.
  24. J. A. Carrillo, F. Filbet, M. Schmidtchen: Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion. Numerische Mathematik, 2020.
  25. M. Burger, J. A. Carrillo, J.-F. Pietschmann, M. Schmidtchen: Segregation Effects and Gap Formation in Cross-Diffusion Models. Interfaces and Free Boundaries, 2020.
  26. R. Bailo, J. A. Carrillo, H. Murakawa, M. Schmidtchen: Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations. M3AS, 2020.
  27. J. A. Carrillo, S. Fagioli, F. Santambrogio, M. Schmidtchen: Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems. SIMA, 50(5), 5695–5718, 2018.
  28. J. A. Carrillo, Y. Huang, M. Schmidtchen: Zoology of a Nonlocal Cross-Diffusion Model for Two Species. SIAP, 2018.
  29. M. Schmidtchen, O. Tse, S. Wackerle: A Multiscale Approach for Spatially Inhomogeneous Disease Dynamics. Commun Biomathematical Sci, 2018.

Preprints

  1. T. Dębiec, V. V. Neumann, M. Schmidtchen: Incompressible limit for a two-species Brinkman model with drift. arXiv:2608.27686, 2026.
  2. J. Hauser, H. Murakawa, M. Schmidtchen: Convergence of a discrete-in-time approximation to a degenerate parabolic-hyperbolic system. arXiv:2606.05879, 2026.