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.

中文翻译：

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具有平均曲率算子的粘性守恒律解的稳定性和动力学

在本文中，我们研究了具有饱和非线性扩散的标量守恒定律的初边值问题解的长期动力学。在讨论了唯一平稳解的存在性及其渐近稳定性之后，我们将注意力集中在亚稳现象上，由此，时变解在相对较短的时间内发展为分层函数，然后在很长的时间内接近稳态时间间隔。数值模拟说明了结果。