Roughness in surface growth equations. (English) Zbl 0989.35147
Summary: 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 \(L^2\)-norm. Our main results describe the growth of the mean interface width for linear stochastic partial differential equations perturbed by white or colored noise.
MSC:
35R60 | PDEs with randomness, stochastic partial differential equations |
74E15 | Crystalline structure |
82D25 | Statistical mechanics of crystals |