@article{Zhao2023, 
author = {Xu Zhao and Wenshu Zhou},
title = {Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {10},
pages = {6505-6524},
keywords = {Hyperbolic system, global large solution, vanishing diffusion limit, boundary layer, BL-thickness},
url = {https://www.sciopen.com/article/10.3934/era.2023329},
doi = {10.3934/era.2023329},
abstract = {We consider an initial and boundary value problem for a nonlinear hyperbolic system with damping and diffusion. This system was derived from the Rayleigh–Benard equation. Based on a new observation of the structure of the system, two identities are found; then, the following results are proved by using the energy method. First, the well-posedness of the global large solution is established; then, the limit with a boundary layer as some diffusion coefficient tending to zero is justified. In addition, the        L    2   convergence rate in terms of the diffusion coefficient is obtained together with the estimation of the thickness of the boundary layer.}
}