2007/11/25 by Guillaume Bal, Bal, Guillaume, Olivier Pinaud +1
Engineering · Mathematics · Physics and Astronomy · #35L05 #35Q40 #60H25 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Random lasers and scattering media #Ultrasonics and Acoustic Wave Propagation #math-ph #math.AP #math.MP #msc:35L05 #msc:35Q40 #msc:60H25
paper · pdf · doi:10.48550/arxiv.0711.3920
arxiv created 2007/11/25 · openalex publication_date 2007/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy density, i.e., by its sensitivity to changes in the realization of the underlying heterogeneous medium modeled as a random medium. In the simplified Itô-Schrödinger regime of wave propagation, we obtain optimal estimates for the statistical instability of the wave energy density for different configurations of the source terms and the domains over which the energy density is measured. We show that the energy density is asymptotically statistically stable (self-averaging) in many configurations. In the case of highly localized source terms, we obtain an explicit asymptotic expression for the scintillation function in the high frequency limit.