Christina Lienstromberg

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.

Wintersemester 2022/23:

Vorlesung mit Übung, Unterrichtssprache Englisch: Analytische Halbgruppen

Content of the course:
Important questions in the study of PDEs are those for existence, uniqueness and qualitative behaviour of solutions. In this lecture the focus is on parabolic PDEs and the theory of analytic semigroups as a tool to obtain answers for these questions. The main idea of semigroup theory in this context is to interpret a given PDE as an abstract ODE in an infinite dimensional Banach space. We will see that solutions of linear evolution equations are constructed by a semigroup which may be seen as a generalisation of the matrix exponential for unbounded operators on Banach spaces.
The aim of this lecture course is to give an insight into parts of the basic theory of analytic semigroups and how this theory may be used to solve parabolic evolution equations. We first introduce some fundamental results on analytic semigroups and their infinitesimal generators. Then the lecture is mainly concerned with applications of this theory in the qualitative analysis of parabolic PDEs.
 
Prerequisites:
Basic notions of functional analysis and PDEs should be known. Knowledge on strongly continuous semigroups and hyperbolic PDEs is helpful but not necessary.
 

Sommersemester 2022:

- Mastervorlesung aus dem Bereich Analysis: Strongly continuous semigroups and hyperbolic evolution equations. (Lehrsprache: Englisch, Darbietungsform: online über Webex, weitere Informationen)

- Masterseminar: Thin-film flows with non-trivial dynamics (Lehrsprache: Englisch, Darbietungsform: online über Webex, weitere Informationen)