The mathematical description of dynamical processes in terms of time-dependent partial differential equations (PDEs) plays a fundamental role in many areas of science. In many models nonlinearities appear naturally due to self-reinforcing processes. If the nonlinear effects dominate smoothing mechanisms such as dissipation or dispersion singularities may form in finite time. In such a scenario, also referred to as 'blowup', the amplitude of the solution diverges or discontinuities are formed. On the one hand, this may indicate certain limitations in the underlying modelling assumptions, i.e., there is no blowup in the real world system. However, in many cases mathematical singularities correspond to physical phenomena such as shock waves in hydrodynamics, light focussing in nonlinear fibre optics or the formation of black holes in gravitational collapse. This motivates the mathematical study of the details of singularity formation in nonlinear PDEs.

Our group focuses on the investigation of blowup dynamics in nonlinear wave equations and heat flows in the so-called energy supercritical case. We mainly use tools from functional analysis, operator theory and spectral analysis as well as ODE methods.

## Current members

Birgit Schörkhuber (head)

David Lichti (PhD student)

## Recent preprints

I. Glogic, B. Schörkhuber.

Co-dimension one stable blowup for the supercritical cubic wave equation.

arXiv preprint 2018.

P. Biernat, R. Donninger and B. Schörkhuber.

Hyperboloidal similarity coordinates and a globally stable blowup profile for supercritical wave maps.

arXiv preprint 2017.

## Events at KIT

25.10.2018: Talk by Hatem Zaag "Blow-up for the Complex Ginzburg-Landau in some critical case"

23.07.2018: Minisympsium Nonlinear dispersive equations - blowup, solitons and long-time behavior at the* Conference on Mathematics of Wave Phenomena*, Department of Mathematics, KIT (organized by B. Schörkhuber)

Name | Tel. | |
---|---|---|

M.Sc. David Lichti | +49 721 608 48728 | david.lichti@kit.edu |

Dr. Birgit Schörkhuber | +43 721 608 46197 | birgit.schoerkhuber@kit.edu |