We study the asymptotic behaviour of solutions to a scalar conservation law with a mean curvature's type diffusion, focusing our attention to the stability/metastability properties of the steady state. In particular, we show the existence of a unique steady state that slowly converges to its asymptotic configuration, with a speed rate which is exponentially small with respect to the viscosity parameter epsilon; the rigorous results are also validated by numerical simulations.
A note on the slow convergence of solutions to conservation laws with mean curvature diffusions
Strani M.
2019
Abstract
We study the asymptotic behaviour of solutions to a scalar conservation law with a mean curvature's type diffusion, focusing our attention to the stability/metastability properties of the steady state. In particular, we show the existence of a unique steady state that slowly converges to its asymptotic configuration, with a speed rate which is exponentially small with respect to the viscosity parameter epsilon; the rigorous results are also validated by numerical simulations.
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