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 |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023329?viewType=HTML |
| _version_ | 1797449804445384704 |
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| author | Xu Zhao Wenshu Zhou |
| author_facet | Xu Zhao Wenshu Zhou |
| author_sort | Xu Zhao |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T14:31:20Z |
| format | Article |
| id | doaj.art-00a0fbfd11e74985a51042504956f90b |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-09T14:31:20Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-00a0fbfd11e74985a51042504956f90b2023-11-28T01:20:24ZengAIMS PressElectronic Research Archive2688-15942023-10-0131106505652410.3934/era.2023329Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusionXu Zhao0Wenshu Zhou 11. School of Mathematics, Jilin University, Changchun 130012, China2. Department of Mathematics, Dalian Minzu University, Dalian 116600, ChinaWe 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.https://www.aimspress.com/article/doi/10.3934/era.2023329?viewType=HTMLhyperbolic systemglobal large solutionvanishing diffusion limitboundary layerbl-thickness |
| spellingShingle | Xu Zhao Wenshu Zhou Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion Electronic Research Archive hyperbolic system global large solution vanishing diffusion limit boundary layer bl-thickness |
| title | Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| title_full | Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| title_fullStr | Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| title_full_unstemmed | Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| title_short | Vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| title_sort | vanishing diffusion limit and boundary layers for a nonlinear hyperbolic system with damping and diffusion |
| topic | hyperbolic system global large solution vanishing diffusion limit boundary layer bl-thickness |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023329?viewType=HTML |
| work_keys_str_mv | AT xuzhao vanishingdiffusionlimitandboundarylayersforanonlinearhyperbolicsystemwithdampinganddiffusion AT wenshuzhou vanishingdiffusionlimitandboundarylayersforanonlinearhyperbolicsystemwithdampinganddiffusion |