Applied Analysis Seminar - Abstracts
Talk
Thursday, 11 November 2021, 13:00-14:00 in HG00.506
Manuel Gnann (TU Delft)
Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations
Abstract
We consider the stochastic FitzHugh-Nagumo equations, whose deterministic equivalent allows for
fast and stable traveling-pulse solutions. In this talk, we investigate the stability of fast
pulses in case of additive noise and derive a multiscale decomposition for small levels of the
stochastic forcing. Our method is based on adapting the wave velocity by solving a stochastic
ordinary differential equation and tracking perturbations of the wave meeting a stochastic
partial differential equation coupled to an ordinary differential equation. Previous works
have focused on applying this method to scalar equations, such as the stochastic Nagumo equation,
which carry a self-adjoint structure. This structure is lost in case of the FitzHugh-Nagumo system
and the linearization does not generate an analytic semigroup. We show that this problem can be
overcome by making use of Riesz spectral projections in a certain way. This provides a major
generalization as our approach appears to be applicable also to general stochastic nerve-axon
equations, the stochastic periodically-forced NLS equation, or systems of stochastic
reaction-diffusion equations.
The talk is based on joint work with Katharina Eichinger (CEREMADE, Université Paris Dauphine)
and Christian Kuehn (Technical University of Munich).
(
back
to Applied Analysis Seminar homepage)