Amplitude equations for stochastic Swift-Hohenberg equatio

  • Luigi Amedeo Bianchi (TU Berlin)
A3 01 (Sophus-Lie room)


We consider a mathematical model for the Rayleigh-Benard convection, the stochastic Swift-Hohenberg equation: \[ \partial_t u = -(1+\partial_x^2)^2u+\varepsilon^2\nu u-u^3+\varepsilon^{\frac{3}{2}}\xi(t,x). \] Near its change of stability, the fluid's motion can be described in a multiscale setting as the product of a slowly varying amplitude equation and a faster periodic wave. After an introduction to the problem in its deterministic setting, we'll review some known stochastic results and see some recent developments in the unbounded space domain setting.

Katja Heid

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