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.
Marta Strani (Corresponding)
|Data di pubblicazione:||2019|
|Titolo:||Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator|
|Rivista:||JOURNAL OF EVOLUTION EQUATIONS|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00028-019-00528-2|
|Appare nelle tipologie:||2.1 Articolo su rivista |