Kathrin Hellmuth

• Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
  Kinetic chemotaxis tumbling kernel determined from macroscopic quantities
  submitted (2022)
   
• Kathrin Hellmuth, Christian Klingenberg
  Computing Black Scholes with Uncertain Volatility—A Machine Learning Approach
  Mathematics, vol. 10, no. 3, 489, special issue "Numerical Analysis with Applications in Machine Learning" (2022)
   
• Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
  Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
  Computation, vol. 9, no. 11, 119, special issue "Inverse Problems with Partial Data” (2021)
   

Conference proceedings:

• Kathrin Hellmuth, Christian Klingenberg, Qin Li
  Multi-scale PDE inverse problem in bacterial movement
  Proceedings of HYP 2022 (2023)
   
• Kathrin Hellmuth
  Inverse problems for kinetic equations - an application to chemotaxis
  Oberwolfach Reports.  Rep. 18 (2021), no. 3, pp. 2316–2318
   
• Kathrin Hellmuth
  An inverse problem for chemotaxis
  Oberwolfach Reports.  Rep. 18 (2021), no. 2, pp. 1080–1083

Science communication:

• Kathrin Hellmuth, Christian Klingenberg
  Route planning for bacteria
  'Snapshots of modern mathematics from Oberwolfach' (2022), no.12

Various natural phenomena can be described using partial differential equations (PDEs). One example is the movement of bacteria stimulated by a chemical signal, which is called chemotaxis. It is often modelled by a kinetic chemotaxis equation or a macroscopic Keller Segel equation and there exists a relation between both PDE models.

In order fit the mathematical models to reality, experiments have to be conducted in order to determine the model coefficients. For chemotaxis, this means observing the bacterial motion so to reconstruct coefficients encoding the bacterial reaction to the chemical substance. I study this inverse problem, in particulat the relation between the inverse problems for the macroscopic and the kinetic model.