| Contents |
| In this talk we will consider the stochastic Swift Hohenberg equation
\[
\frac{\partial u}{\partial t} = -(1+\partial_x^2)^2u + \epsilon^2\nu u -u^3 +\epsilon^{3/2}\xi(t,x)
\]
in an unbounded domain, where the noise $\xi$ is a space-time white noise.
Close to the change of stability at $\nu=0$ we can describe the solution $u$ of the equation as a modulated wave
\[
u(t,x) = \epsilon\mathcal{A}(\epsilon^2 t,\epsilon x)e^{ix} + \textrm{c.c.}
\]
We derive this so called amplitude equation, which is a Ginzburg Landau equation.
As a first case we limit ourselves to the linear problem. |
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