scholarly journals Convergence and center manifolds for differential equations driven by colored noise

2019 ◽  
Vol 39 (8) ◽  
pp. 4797-4840
Author(s):  
Jun Shen ◽  
◽  
Kening Lu ◽  
Bixiang Wang ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Colored Noise ◽  
Center Manifolds

SURFACE ROUGHNESS IN MOLECULAR BEAM EPITAXY

2001 ◽  
Vol 01 (02) ◽  
pp. 239-260 ◽  
Author(s):  
DIRK BLÖMKER ◽  
STANISLAUS MAIER-PAAPE ◽  
THOMAS WANNER
Keyword(s):  
Surface Roughness ◽  
Partial Differential Equations ◽  
Molecular Beam Epitaxy ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Molecular Beam ◽  
Colored Noise ◽  
Partial Differential ◽  
Interface Width ◽  
The Mean

This paper discusses the roughness of surfaces described by nonlinear stochastic partial differential equations on bounded domains. Roughness is an important characteristic for processes arising in molecular beam epitaxy, and is usually described by the mean interface width of the surface, i.e. the expected value of the squared Lebesgue norm. By employing results on the mean interface width for linear stochastic partial differential equations perturbed by colored noise, which have been previously obtained, we describe the evolution of the surface roughness for two classes of nonlinear equations, asymptotically both for small and large times.

Sign in / Sign up

Export Citation Format

Share Document