Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion

Autor:	Xu Zhao, Wenshu Zhou
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	hyperbolic system global large solution vanishing diffusion limit boundary layer bl-thickness Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 10, Pp 6505-6524 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023329?viewType=HTML
Popis:	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.
Databáze:	Directory of Open Access Journals
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