Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912172734414848 |
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| author | Huang, Feimin Qiu, Guiqin Wang, Yi Yang, Xiaozhou |
| author_facet | Huang, Feimin Qiu, Guiqin Wang, Yi Yang, Xiaozhou |
| contents | We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation $u_t+uu_x+uu_y=Δu$, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve $y=φ(x)$, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation Huang, Feimin Qiu, Guiqin Wang, Yi Yang, Xiaozhou Analysis of PDEs We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation $u_t+uu_x+uu_y=Δu$, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve $y=φ(x)$, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large. |
| title | Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.20957 |