Stephan GersterInstitut für Geometrie und Praktische Mathematik
phone:+49 241 80-94 559
TeachingMathematik I & II (für Bau-, Umwelt-, Wirtschafts-, Verkehrsingenieurwesen)
- Stochastic Galerkin Formulations for Hyperbolic Balance Laws Stochastic Galerkin methods reformulate a stochastic system as a deterministic one that describes the evolution of polynomial chaos modes. So far, results for general hyperbolic systems are not available. A problem is posed by the fact that the deterministic Jacobian of the projected system differs from the random Jacobian of the original system and hence hyperbolicity is not guaranteed. We show for some fluid-dynamic and kinetic equations hyperbolicity, wellposedness and energy estimates.
- Feedback Control for Hyperbolic Systems Physical systems such as water and gas networks are usually operated in a state of equilibrium and feedback control is employed to damp small perturbations over time. We consider problems on networks, described by kinetic and hyperbolic balance laws, and analyze their stability.
- Stochastic Fluctuations in Energy Networks The ability of gas-fired power plants to ramp quickly is used to balance fluctuations in the power grid caused by renewable energy sources, which in turn leads to time-varying gas consumption and fluctuations in the gas network. Since gas system operators assume nearly constant gas consumption, there is a need to assess the risk of these stochastic fluctuations. We discuss control policies to damp fluctuations in the network.
Stephan Gerster, Michael Herty, Hui Yu, Hypocoercivity of stochastic Galerkin formulations for stabilization of kinetic equations, RWTH-preprint, No. 503, 2020
Torsten Trimborn, Stephan Gerster, Giuseppe Visconti, Spectral methods to study the robustness of residual neural networks with infinite layers, Foundations of Data Science, 2020
Stephan Gerster, Michael Herty, Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations, Communications in Computational Physics, Vol. 27, 2020
Michael Herty, Stephan Gerster, Stochastic Galerkin Formulations for Hyperbolic Conservation Laws, Oberwolfach Report, No. 24/2019, 2019
Stephan Gerster, Michael Herty, Aleksey Sikstel, Hyperbolic Stochastic Galerkin Formulation for the p-System, Journal of Computational Physics, Vol. 395, 2019
Martin Gugat, Stephan Gerster, On the Limits of Stabilizability for Networks of Strings, Systems & Control Letters, Vol. 131, 2019
Stephan Gerster, Michael Herty, Discretized Feedback Control for Systems of Linearized Hyperbolic Balance Laws, Mathematial Control & Related Fields, Vol. 9, No 3, 2019
Stephan Gerster, Michael Herty, Michael Chertkov, Marc Vuffray, Anatoly Zlotnik, Polynomial Chaos Approach to Describe the Propagation of Uncertainties through Gas Networks, Proceeding in Progress in Industrial Mathematics at ECMI 2018, Springer, 2019
Stephan Gerster, Stabilization of Stochastic Fluctuations in Hyperbolic Systems, to appear as Proceeding in the 21st IFAC World Congress, 2020