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International Conference of Steklov Institute Members, working outside Russia
June 5, 2009 12:30, Moscow
 


Dissipative perturbations of integrable PDE

S. B. Kuksin
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S. B. Kuksin


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Abstract: In the introductory part of my talk I will discuss what is known and unknown about Hamiltonian and dissipative perturbations of an integrable PDE under periodic boundary conditions. Next I will present an averaging theory for such equation, perturbed by a small viscosity and small random force. It turns out that the averaged dynamics is described by a quasilinear stochastic heat equation with a non-local nonlinearity. The theory applies both to solutions of Cauchy problem and to stationary in time solutions.

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