A Pregenerator for Burgers Equation¶Forced by Conservative Noise |
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| Authors: | Sigurd Assing |
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| Institution: | (1) Department of Mathematics and Statistics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK. E-mail: assing@maths.ed.ac.uk, GB |
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| Abstract: | We consider the stationarity of a Burgers equation with an external random force of gradient type in one space dimension.
The expected stationary measure is the white noise measure on the space of tempered distributions. As a consequence, the nonlinearity
of the formal equation u
t
+λu
u
x
=νu
xx
+η
x
is ill-defined. Introducing a pregenerator we can formulate a generalized martingale problem leading to a meaningful version
of the formal equation which was an open problem.
Received: 9 March 2001 / Accepted: 10 October 2001 |
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| Keywords: | |
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