Contact:

Birgit Schörkhuber
University of Innsbruck
Dep. of Mathematics
Technikerstraße 13
6020 Innsbruck
Austria

Tel: +43 512 507 53910

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.

Members

Univ. Prof. Dr. Birgit Schörkhuber

Dr. Elek Csobo

(Postdoctoral researcher)

Sarah Kistner

(PhD student, to start with March 2022)

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

Michael McNulty, PhD student at UC Riverside, USA

jointly supervised by Po-Ning Chen (UCR) and Birgit Schörkhuber

Recent publications

Elek Csobo, Irfan Glogić and Birgit Schörkhuber. On blowup for the supercritical quadratic wave equation. arXiv 2109.11931

Irfan Glogić and Birgit Schörkhuber. Co-dimension one stable blowup for the supercritical cubic wave equation. Adv. Math. (390) 2021

Teaching (Winter 2021/22)

VO Partielle Differentialgleichungen (B. Schörkhuber)
PS Partielle Differentialgleichungen (B. Schörkhuber)
VU Aspects of Nonlinear Wave Equations (B. Schörkhuber)
PS Lineare Algebra (E. Csobo)

Teaching (Summer 2022)

VO Analysis 1 (B. Schörkhuber)
PS Analysis 1 (B. Schörkhuber)
SE Critical Research Analysis: Analysis of nonlinear time-dependent PDEs (B. Schörkhuber)
PS Analysis 2 for Prospective Teachers (E. Csobo)

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

Activities

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