Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion
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 us...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023329?viewType=HTML |
| Summary: | 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. |
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| ISSN: | 2688-1594 |