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
- With S. Schiffer & R. Schubert: A data-driven approach to viscous fluid mechanics -- the stationary case, arXiv:2207.00324, 2022.
- With J. Jansen & K. Nik: Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order; arXiv:2204.08231, 2022.
- 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.
- With O. Assenmacher & G. Bruell: Non-Newtonian two-phase thin-film problem: Local existence, uniqueness, and stability; Comm. PDE 47, pp. 197--232, 2021.
- 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.
- 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.
- With Stefan Müller: Local strong solutions to a quasilinear degenerate fourth-order thin-film equation. NoDEA. 27, 2020.
- With J. Escher: Travelling waves in dilatant non-Newtonian thin films; J. Differential Equations 264, pp. 2113–2132, 2018.
- 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.
- With J. Escher & P. Gosselet: A note on model reduction for microelectromechanical systems. Nonlinearity 30, pp. 454–465, 2017.
- Well-posedness of a quasilinear evolution problem modelling MEMS with general permittivity. J. Evol. Equ. 17, pp. 1129–1150, 2017.
- With J. Escher: Finite-time singularities of solutions to microelectromechanical systems with general permittivity. Ann. Mat. Pura Appl. 195, pp. 1961–1976, 2016.
- On qualitative properties of solutions to microelectromechanical systems with general permittivity. Monatsh. Math. 179, pp. 581–602, 2016.
- With J. Escher: A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile. Comm. PDE 41, pp. 134–149, 2016.
- A free boundary value problem modelling microelectromechanical systems with general permittivity. Nonlinear Anal. Real World Appl. 25, pp. 190–218, 2015.
