Contact:

Birgit Schörkhuber
Universität Innsbruck
Institut für Mathematik
Technikerstraße 13
6020 Innsbruck
Austria

Mail: birgit.schoerkhuber@uibk.ac.at 

Analysis of PDEs

Welcome!

Our group Analysis of Partial Differential Equations (Analysis of PDEs) has recently  been established  as a new research direction at the Institute of Mathematics.

The description of dynamics in terms of partial differential equations (PDEs) plays a fundamental role in physical theories, natural  sciences and applications.  In many models nonlinearities appear naturally due to self-reinforcing processes. Despite the huge variety of problems described by nonlinear PDEs, the mathematical understanding of such problems is still limited. Consequently, the development of new analytic tools is a challenging and very active area of mathematical research.

In our group, we are mainly interested in time-evolution problems, where we investigate questions concerning local and global existence, the formation of singularities in finite time and the existence and stability of special solutions. Thereby we focus on nonlinear wave equations,  Schrödinger equations and heat flows.

In our work, we are using a variety of analytic techniques, in particular tools from functional analysis, operator theory, and spectral analysis as well as ODE methods. 

If you are interested in topics for Bachelor/master thesis, please contact us!

Members 

Birgit Schörkhuber

Christina Bailey (Administrative Staff)

Akansha Sanwal (Postdoctoral researcher)

Sarah Kistner (PhD student)

Associated Members 

Alexander Wittenstein, PhD student at KIT, Karlsruhe, Germany

jointly supervised by Tobias Lamm (KIT) and Birgit Schörkhuber within the project B5 "Geometric Wave Equations" CRC 1173

Recent Publications 

• Po-Ning Chen, Michael McNulty and Birgit Schörkhuber. Singularity formation for the higher dimensional Skyrme model in the strong field limit. (Submitted) 
  arXiv:2310.07042 
  
  
• Irfan Glogić, Sarah Kistner and Birgit Schörkhuber. Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions. (Submitted)
  arXiv 2304.04104
  
  
• Irfan Glogić and Birgit Schörkhuber.  Stable singularity formation for the Keller-Segel system in three dimensions. 
  Archive for Rational Mechanics and Analysis (accepted 2023)
  arXiv 2209.11206 
  
  
• Po-Ning Chen, Roland Donninger, Irfan Glogić, Michael McNulty and Birgit Schörkhuber.  Co-dimension one stable blowup for the quadratic wave equation beyond the light cone. 
  Communications in Mathematical Physics (accepted 2023)
  arXiv 2209.07905
  
  
• Elek Csobo, Irfan Glogić and Birgit Schörkhuber. On blowup for the supercritical quadratic wave equation.
  Analysis & PDE (accepted 2022, to appear)
  arXiv 2109.11931
  
  
• Irfan Glogić and Birgit Schörkhuber. Co-dimension one stable blowup for the supercritical cubic wave equation.
  Advances in Mathematics
  Adv. Math. (390) 2021 
  

Organization of Workshop and Summer Schools

• Thematic Programme Nonlinear Waves and Relativity , Erwin Schrödinger Institute, Vienna, Austria, April 29 - June 21, 2024
  (together with Roland Donninger and David Fajman)
  
  
• BIRS Workshop Women in nonlinear dispersive PDEs, Banff International Research Station, Canada, February 5 -10, 2023
  (together with Mihaela Ifrim and Katharina Schratz)
  
  

• Summer School Geometric Dispersive PDEs , Obergurgel, Austria, September 25 - 30, 2022
  (together with Tobias Lamm and Tobias Weth)

• Mini-Symposium Blow-up and Global Dynamics in Nonlinear Dispersive PDEs at the Conference of Mathematics of Wave Phenomena, 14.-18.02.2022  (together with Sebastian Herr)
  

PDE Seminar 

• Analysis and Numerics of PDEs (organised together with Alexander Ostermann and Heiko Gimperlein)