Research

 

Research Interests (Applied Analysis)

  • Partial differential equations
  • Free boundary value problems
  • Modelling and analysis of non-Newtonian thin fluid films
  • Modelling and analysis of MEMS

 

Publications

  1. With S. Schiffer & R. Schubert: A data-driven approach to viscous fluid mechanics -- the stationary case, arXiv:2207.00324, 2022.
  2. With J. Jansen & K. Nik: Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order; arXiv:2204.08231, 2022.
  3. With J. J. L. Velázquez: Long-time asymptotics and regularity estimates for weak solutions to a doubly-degenerate  thin-film equation in the Taylor-Couette setting, arxiv:2203.00075, 2022.
  4. With O. Assenmacher & G. Bruell: Non-Newtonian two-phase thin-film problem: Local existence, uniqueness, and stability; Comm. PDE 47, pp. 197--232, 2021.
  5. With T. Pernas-Castaño & J. J. L. Velázquez: Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid; J. Nonlinear Sci. 32, 2021.
  6. With J. Escher, P. Knopf & B.-V. Matioc: Stratified periodic water waves with singular density gradients. Ann. Mat. Pura Appl. 199, pp. 1923–1959, 2020.
  7. With Stefan Müller: Local strong solutions to a quasilinear degenerate fourth-order thin-film equation. NoDEA. 27, 2020.
  8. With J. Escher: Travelling waves in dilatant non-Newtonian thin films; J. Differential Equations 264, pp. 2113–2132, 2018.
  9. With J. Escher: A survey on second-order free boundary value problems modelling MEMS with general permittivity. Discrete Contin. Dyn. Syst. Ser S10,  no. 4, pp. 745–771, 2017.
  10. With J. Escher & P. Gosselet: A note on model reduction for microelectromechanical systems. Nonlinearity 30, pp. 454–465, 2017.
  11. Well-posedness of a quasilinear evolution problem modelling MEMS with general permittivity. J. Evol. Equ. 17, pp. 1129–1150, 2017.
  12. With J. Escher: Finite-time singularities of solutions to microelectromechanical systems with general permittivity. Ann. Mat. Pura Appl. 195, pp. 1961–1976, 2016.
  13. On qualitative properties of solutions to microelectromechanical systems with general permittivity. Monatsh. Math. 179, pp. 581–602, 2016.
  14. With J. Escher: A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile. Comm. PDE 41, pp. 134–149, 2016.
  15. A free boundary value problem modelling microelectromechanical systems with general permittivity. Nonlinear Anal. Real World Appl. 25, pp. 190–218, 2015.

Links