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 equations 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 analytic description of the dynamics in time-evolution problems. This concerns local and global existence of solutions, the formation of singularities in finite time and the stability of special solutions. We are working on a wide range of problems including nonlinear dispersive PDEs (e.g. wave equations,  Schrödinger equations) and nonlinear heat flows. 

In our research, we are using a variety of analytic techniques - most importantly tools from functional analysis, operator theory, spectral analysis and ODE theory. 

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 
  • Roland Donninger and Birgit Schörkhuber. Self-similar blowup for the cubic Schrödinger equation. (Submitted) 
    arXiv:2406.16597 

  • Shinya Kinoshita, Akansha Sanwal and Robert Schippa. Improved well-posedness for quasilinear and sharp local well-posedness for semilinear KP-I equations. (Submitted) 
    arXiv:2408.16348

  • 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. 
    Calc. Var. Partial Differential Equations 63 (2024), no. 4, Paper No. 96, 33 pp.

  • Irfan Glogić and Birgit Schörkhuber.  Stable singularity formation for the Keller-Segel system in three dimensions. 
    Arch. Ration. Mech. Anal. 248 (2024), no. 1, Paper No. 4, 40 pp. 

  • 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. 
    Comm. Math. Phys. 405 (2024), no. 2, Paper No. 34, 46 pp

  • Elek Csobo, Irfan Glogić and Birgit Schörkhuber. On blowup for the supercritical quadratic wave equation.
    Anal. PDE 17 (2024), no. 2, 617–680. 

  • Irfan Glogić and Birgit Schörkhuber. Co-dimension one stable blowup for the supercritical cubic wave equation.
    Adv. Math. 390 (2021), Paper No. 107930, 79 pp.

Organization of Workshop and Summer Schools
PDE Seminar 


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