A semigroup approach for stochastic quasilinear equations driven by rough noise |
Alexandra Blessing, Universität Konstanz |
Friday, 2024-06-14 08:00 |
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We consider stochastic quasilinear equations perturbed by nonlinear multiplicative noise. Ex-ploring semigroup methods and combining techniques from functional analysis with tools from rough path theory, we establish the pathwise well-posedness of such equations. We apply our results to the stochastic Shigesada-Kawasaki-Teramoto equation describing population segregation by induced cross-diffusion and to the Landau-Lifshitz-Gilbert equation which models the magnetization of a ferromagnetic material. Moreover, we emphasize the advantage of rough path theory in the study of the long-time behavior of such systems. This talk is based on joint works with Antoine Hocquet and Christian Kuehn. |