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July 2013 The Burgers equation with Poisson random forcing
Yuri Bakhtin
Ann. Probab. 41(4): 2961-2989 (July 2013). DOI: 10.1214/12-AOP747


We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case.


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Yuri Bakhtin. "The Burgers equation with Poisson random forcing." Ann. Probab. 41 (4) 2961 - 2989, July 2013.


Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1286.60099
MathSciNet: MR3112935
Digital Object Identifier: 10.1214/12-AOP747

Primary: 37L55 , 60H15 , 60K37
Secondary: 60G55

Keywords: ergodicity , global solution , one force—one solution principle , one-point attractor , Poisson point process , random environment , random forcing , The Burgers equation , Variational principle

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 4 • July 2013
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