.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.
Publié le : 1997-01-14
Classification:
Wave equation,
white noise,
stochastic partial differential equations,
60H15,
35R60,
35L05
@article{1024404282,
author = {Mueller, Carl},
title = {Long time existence for the wave equation with a noise
term},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 133-151},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404282}
}
Mueller, Carl. Long time existence for the wave equation with a noise
term. Ann. Probab., Tome 25 (1997) no. 4, pp. 133-151. http://gdmltest.u-ga.fr/item/1024404282/