Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator
Analysis of PDEs
2024-05-21 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1805.12416,
title = {Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator},
author = {Raffaele Folino and Maurizio Garrione and Marta Strani},
journal= {arXiv preprint arXiv:1805.12416},
year = {2024}
}
Comments
28 pages, 9 figures