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Article Dans Une Revue Potential Analysis Année : 2007

m-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise

Giuseppe da Prato
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Résumé

In this article, we prove that the Kolmogorov operator associated to the Burgers equation driven by a space-time white noise is m-dissipative. This implies several properties on the Kolmogorov equation.This result is obtained thanks to the introduction of a modified Kolmogorov operator. New a priori estimates on the solutions of the Burgers equation and on the invariant measure are obtained. These are crucial in our argument.
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Dates et versions

hal-00001354 , version 1 (25-03-2004)

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Giuseppe da Prato, Arnaud Debussche. m-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Potential Analysis, 2007, 26 (1), pp.31-55. ⟨10.1007/s11118-006-9021-5⟩. ⟨hal-00001354⟩
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