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On nonlinear amplitude evolution under stochastic forcing
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DOI：10.1016/S0096-3003(99)00016-8.png)
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The complex Ginzburg-Landau amplitude equation, with or without random forcing, arises as approximate reductions of complicated physical systems on extended spatial domains near bifurcation points. Unlike the deterministic Ginzburg-Landau equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced Ginzburg-Landau equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions. (C) 2000 Elsevier Science Inc. All rights reserved.
Keyword:
stochastic forcing
stochastic partial differential equation
amplitude equation
infinite dimensional dynamical system
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