Katharina Eichinger (CEREMADE, Université Paris-Dauphine, France): Multiscale analysis of the stochastic FitzHugh-Nagumo equations
Ort: MPI für Mathematik in den Naturwissenschaften Leipzig, , Videobroadcast
We investigate the stability of traveling-pulse solutions to thestochastic FitzHughNagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a stochastic ordinary differential equation (SODE) and tracking perturbations to the wave meeting a stochastic partial differential equation (SPDE) coupled to an ordinary differential equation (ODE). This approach has been employed by Krüger and Stannat  for scalar stochastic bistable reaction-diffusion equations such as the Nagumo equation. A main difference in our situation of an SPDE coupled to an ODE is that the linearization around the traveling wave is not self-adjoint anymore, so that fluctuations around the wave cannot be expected to be orthogonal in a corresponding inner product. We demonstrate that this problem can be overcome by making use of Riesz instead of orthogonal spectral projections. We expect that our approach can also be applied to traveling waves and other patterns in more general situations such as systems of SPDEs that are not self-adjoint. This provides a major generalization as these systems are prevalent in many applications. This is joint work with Manuel Gnann and Christian Kuehn. <br />One day before the seminar, an announcement with the Zoom link will be sent to those who registered with Zachary Adams. For this please contact him at <a href="mailto:firstname.lastname@example.org">Zachary Adams</a>.
Beginn: 1. Juni 2020 15:00
Ende: 1. Juni 2020 16:30