Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator

In this paper we study the long time dynamics of the solutions to an 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 phenomen...

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Bibliographic Details
Published in:Journal of evolution equations 2020-06, Vol.20 (2), p.517-551
Main Authors: Folino, Raffaele, Garrione, Maurizio, Strani, Marta
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Computer simulation
Conservation laws
Dynamic stability
Mathematics
Mathematics and Statistics
Time dependence
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Summary:In this paper we study the long time dynamics of the solutions to an 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.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-019-00528-2