Small noise asymptotic expansion for the infinite dimensional Van der Pol oscillator

摘要

We consider a forced reaction diffusion model of the Van der Pol type oscillator taking values in a suitable infinite dimensional Hilbert space H, subjected to boundary Neumann conditions and randomly perturbed by a small intensity parameter ∈. We provide an asymptotic expansions of the related solution to all orders in the parameter ∈, explicitly writing the expansion coefficients and the remainder.