Research Interests
$\bullet$ Mathematical modelling.
$\bullet$ Nonlinear partial differential equations and their qualitative analysis.
$\bullet$ Interacting particle systems.
$\bullet$ Limiting procedures.
Selected Publications of Prof. Dr. Angela Stevens
$\bullet$ A. Scheel, A. Stevens, and C. Tenbrock. Signaling gradients in surface dynamics as basis for planarian regeneration. J. Math. Biol., 83(1):paper no.6, 31pp, 2021.
$\bullet$ G. Kaib, K. Kang, and A. Stevens. Global minimizers for anisotropic attractive-repulsive interactions. European J. Appl. Math., 31(5):854-870, 2019.
$\bullet$ K. Kang, A. Scheel, and A. Stevens. Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup. Nonlinearity, 32(6):2128–2146, 2019.
$\bullet$ A. Scheel and A. Stevens. Wavenumber selection in coupled transport equations. J. Math. Biol., 75(5):1047–1073, 2017.
$\bullet$ S. Grosskinsky, D. Marahrens, and A. Stevens. A hydrodynamic limit for chemotaxis in a given heterogeneous environment. Vietnam J. Math., 45(1):127–152, 2017.
$\bullet$ J. Fuhrmann and A. Stevens. A free boundary problem for cell motion. Differential Integral Equations, 28(7/8):695–732, 2015.
$\bullet$ I. Primi, A. Stevens, and J. J. L. Velázquez. Pattern forming instabilities driven by non-diffusive interactions. Netw. Heterog. Media, 8(1):397–432, 2013.
$\bullet$ I. Primi, A. Stevens, and J. J. L. Velázquez. Mass-selection in alignment models with non-deterministic effects. Comm. Partial Differential Equations, 34(5):419–456, 2009.
$\bullet$ E. E. Espejo Arenas, A. Stevens, and J. J. L. Velázquez. Simultaneous finite time blow-up in a two-species model for chemotaxis. Analysis, 29(3):317–338, 2009.
$\bullet$ H. J. Hwang, K. Kang, and A. Stevens. Global solutions of nonlinear transport equations for chemosensitive movement. SIAM J. Math. Anal., 36(4):1177–1199, 2005.
$\bullet$ S. Heinze, G. Papanicolaou, and A. Stevens. Variational principles for propagation speeds in inhomogeneous media. SIAM J. Appl. Math., 62(1):129–148, 2001.
$\bullet$ A. Stevens. The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. SIAM J. Appl. Math., 61(1):183–212, 2000.
$\bullet$ H. G. Othmer and A. Stevens. Aggregation, blowup, and collapse: the {ABC}s of taxis in reinforced random walks. SIAM J. Appl. Math., 57(4):1044–1081, 1997.
Recent Publications of Prof. Dr. Angela Stevens
$\bullet $ Stephan Luckhaus and Angela Stevens. A free boundary problem-in time-for the spread of Covid-19. Journal of Mathematical Biology, 86(3):45, February 2023. doi:10.1007/s00285-023-01881-0.
$\bullet $ Stephan Luckhaus and Angela Stevens. A two level contagion process and its deterministic McKendrick limit with relevance for the Covid epidemic. Ensaios Matemáticos, 2023. doi:10.21711/217504322023/em3813.
$\bullet $ Stephan Luckhaus and Angela Stevens. Kermack and McKendrick Models on a Two-Scale Network and Connections to the Boltzmann Equations, pages 417–427. Lecture Notes in Mathematics. Springer International Publishing, January 2023. doi:10.1007/978-3-031-12244-6_29.
$\bullet $ Angela Stevens and Michael Winkler. Taxis-driven persistent localization in a degenerate Keller-Segel system. Commun. Part. Diff. Eq., 47(12):2341–2362, October 2022. doi:10.1080/03605302.2022.2122836.
$\bullet $ Arnd Scheel and Angela Stevens. Regeneration of tissue: Lessons learned from flatworms. SIAM News, October 2021. URL: https://www.siam.org/publications/siam-news/articles/regeneration-of-tissue-lessons-learned-from-flatworms/.
$\bullet $ Gunnar Kaib, Kyungkeun Kang, and Angela Stevens. Global minimizers for anisotropic attractive-repulsive interactions. Eur. J. Appl. Math., pages 1–17, October 2019. doi:10.1017/s0956792519000299.
$\bullet $ Kyungkeun Kang, Arnd Scheel, and Angela Stevens. Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup. Nonlinearity, 32(6):2128–2146, May 2019. doi:10.1088/1361-6544/ab046d.