25 citations · 68 across the 14 of their papers we have counts for
5 papers · 1 filter
Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions
Peter Hochs, A. J. Roberts
We prove that a general class of nonlinear, non-autonomous ODEs in Fréchet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal fo…
On the approximation for singularly perturbed stochastic wave equations
Wei Wang, Yan Lv, A. J. Roberts
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations νu_{tt}+u_t…
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
Yan Lv, A. J. Roberts
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation νu_{tt}+u_t=\D u+f(u)+ν^α\dot{W} on…
Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain
Wei Wang, A. J. Roberts
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically s…
Average and deviation for slow-fast stochastic partial differential equations
W. Wang, A. J. Roberts
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a clas…