3 years ago

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

Raffaele Folino, Maurizio Garrione, Marta Strani

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.

Publisher URL: http://arxiv.org/abs/1805.12416

DOI: arXiv:1805.12416v2

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