Analysis of PDEs

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Welcome!

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 as well as the existence and stability of special solutions. We are working on a wide range of problems including nonlinear dispersive PDEs (e.g. wave equations,  Schrödinger equations), nonlinear heat flows and other models.

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!

Contact:

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

Mail: birgit.schoerkhuber@uibk.ac.at 

Members

Birgit Schörkhuber

Christina Bailey (Administrative Staff)

Xueqin Peng (Postdoctoral researcher)

Akansha Sanwal (Postdoctoral researcher)

Sarah Kistner (PhD student)

Recent Publications

  • Johannes Angerer, Sarah Kistner and Birgit Schörkhuber. Existence of a stable shrinker for the corotational harmonic map heat flow in higher space dimensions.
    arXiv:2607.27072
     

  • Akansha Sanwal, Birgit Schörkhuber and David Wallauch. Stability of global self-similar solutions to the cubic wave equation and the wave maps equation.
    arXiv 2607.02493 
     
  •  Irfan Glogić, Sarah Kistner and Birgit Schörkhuber. Stable blowup profile for a semilinear Heat Equation with spatially inhomogeneous nonlinearity.
    arXiv:2604.19389
     
  • Roland Donninger, Birgit Schörkhuber and Alexander Wittenstein. Stable blowup for supercritical wave maps into perturbed spheres. 
    Journal of Functional Analysis 2026, online first (10.1016/j.jfa.2026.111601)
     
  • Roland Donninger and Birgit Schörkhuber. Self-similar blowup for the cubic Schrödinger equation. 
    Communications in Pure and Applied Mathematics 2026, online first (http://doi.org/10.1002/cpa.70042)
     
  • Shinya Kinoshita, Akansha Sanwal and Robert Schippa. Sharp local well-posedness for KP-I equations in the semilinear regime.
    Forum of Mathematics, Sigma , Volume 14 , 2026 
     
  • Shinya Kinoshita, Akansha Sanwal and Robert Schippa. Improved well-posedness for quasilinear and sharp local well-posedness for semilinear KP-I equations. 
    Discrete and Continuous Dynamical Systems, 45.10 (2025): 3625-3661. 
     
  • Po-Ning Chen, Michael McNulty and Birgit Schörkhuber. Singularity formation for the higher dimensional Skyrme model in the strong field limit.
    To appear in Transactions of the AMS, 2026 
    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

Guest lectures

Prof. Dr. Christof Sparber - University of Illinois at Chicago

"Ground state (in-)stability and long-time behavior in multi-dimensional Schrödinger equations"

Tuesday 3rd June 2025, 3.30pm, SR 2 ICT Building, Technikerstraße 21a

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