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Averaging principle for systems of reaction-diffusion equations with polynomial nonlinearities perturbed by multiplicative noise. (English) Zbl 1239.60055
The author studies the averaging principle for a class of systems of two reaction-diffusion equations in a bounded domain \(D\) of \(\mathbb R^d\) (for any \(d \geq 1\)) perturbed by a multiplicative noise, in which the slow and fast motions are both described by an equation having polynomial growth. This model includes systems of reaction-diffusion equations of Fitzhugh-Nagumo or Ginzburg-Landau type perturbed by Gaussian noise.
This is an extension of previous results where a Lipschitz-continuity assumption for the coefficients of the slow and of the fast motions were a crucial ingredient.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
34K33 Averaging for functional-differential equations
35K57 Reaction-diffusion equations
37A25 Ergodicity, mixing, rates of mixing
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
35R60 PDEs with randomness, stochastic partial differential equations
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