Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866911879556759552 |
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| author | Folino, Raffaele Garrione, Maurizio Strani, Marta |
| author_facet | Folino, Raffaele Garrione, Maurizio Strani, Marta |
| contents | In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its asymptotic stability, we focus our attention on the phenomenon of 'metastability', whereby the time-dependent solution develops into a layered function in a relatively short time, and subsequently approaches a steady state in a very long time interval. Numerical simulations illustrate the results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1805_12416 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator Folino, Raffaele Garrione, Maurizio Strani, Marta Analysis of PDEs 35K20, 35B36, 35B40, 35P15 In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its asymptotic stability, we focus our attention on the phenomenon of 'metastability', whereby the time-dependent solution develops into a layered function in a relatively short time, and subsequently approaches a steady state in a very long time interval. Numerical simulations illustrate the results. |
| title | Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator |
| topic | Analysis of PDEs 35K20, 35B36, 35B40, 35P15 |
| url | https://arxiv.org/abs/1805.12416 |