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January 1997 Long time existence for the wave equation with a noise term
Carl Mueller
Ann. Probab. 25(1): 133-151 (January 1997). DOI: 10.1214/aop/1024404282


.1 2 We consider the equation $u_{tt} = \Delta u + a(u) \mathsf{N}$ for $x \epsilon \mathbf{R}^1$ or $R^2$. $\mathsf{N}$ is a Gaussian noise term, which is white noise if $x \epsilon \mathbf{R}^1$. If $a(u)$ grows no faster than $u (\log u)^{1/2-\varepsilon}$, then there is a unique solution valid for all time.


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Carl Mueller. "Long time existence for the wave equation with a noise term." Ann. Probab. 25 (1) 133 - 151, January 1997.


Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0884.60054
MathSciNet: MR1428503
Digital Object Identifier: 10.1214/aop/1024404282

Primary: 60H15
Secondary: 35L05 , 35R60

Keywords: Stochastic partial differential equations , wave equation , White noise

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 1 • January 1997
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