On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| author | Folino, Raffaele Strani, Marta |
| author_facet | Folino, Raffaele Strani, Marta |
| contents | In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monotone) and singular nonlinear diffusions are considered. In particular, the cases of mean curvature-type diffusions both in the Euclidean space and in Lorentz-Minkowski space enter in our framework. After dealing with existence and stability of monotone steady states in a bounded interval of the real line with Dirichlet boundary conditions, we discuss the speed rate of convergence to the asymptotic limit as $t\to+\infty$. Finally, in the particular case of a Burgers flux function, we show that the solutions exhibit the phenomenon of metastability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_05913 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions Folino, Raffaele Strani, Marta Analysis of PDEs In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monotone) and singular nonlinear diffusions are considered. In particular, the cases of mean curvature-type diffusions both in the Euclidean space and in Lorentz-Minkowski space enter in our framework. After dealing with existence and stability of monotone steady states in a bounded interval of the real line with Dirichlet boundary conditions, we discuss the speed rate of convergence to the asymptotic limit as $t\to+\infty$. Finally, in the particular case of a Burgers flux function, we show that the solutions exhibit the phenomenon of metastability. |
| title | On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1904.05913 |