We consider the roughness of surfaces described by stochastic partial differential equations on bounded domains which arise in surface growth equations. The roughness is usually described by the mean interface width, which is the expected value of the squared L2 -norm. Our main results describe the growth of the mean interface width for linear stochastic partial differential equations perturbed by white or colored noise.
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Dirk Blömker, Stanislaus Maier-Paape, Thomas Wanner, Roughness in surface growth equations. Interfaces Free Bound. 3 (2001), no. 4, pp. 465–484DOI 10.4171/IFB/49