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Department of Mathematics

Karlsruhe Institute of Technology
D-76128 Karlsruhe
Germany
Tel.: +49 721 608-43800

Junior Research Group Singularity formation in nonlinear PDEs

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 self-reinforcing processes modelled by nonlinearities can dominate smoothing mechanisms such as dissipation or dispersion. This typically leads to the formation of singularities in finite time. In such a scenario, also referred to as 'blowup', the amplitude of the solution diverges or discontinuities are formed. One 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 hydrodynamcs, 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. However, also numerical experiments can provide important information and shed some light on the behaviour of generic solutions.


Upcoming Events

23.07.2018: Minisympsium on Nonlinear dispersive equations - blowup, solitons and long-time behavior at the Conference on Mathematics of Wave Phenomena, Department of Mathematics, KIT

Staff in the Junior Research Group Nonlinear Helmholtz Equations
Name Tel. E-Mail
+49 721 608 48728 david.lichti@kit.edu
+43 721 608 46197 birgit.schoerkhuber@kit.edu