In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating diffusions (monotone and non monotone) and singular nonlinear diffusions are considered. In particular, the cases of mean curvature-type diffusions both in the Euclidean space and in Lorentz–Minkowski space enter in our framework. After dealing with existence and stability of monotone steady states in a bounded interval of the real line with Dirichlet boundary conditions, we discuss the speed rate of convergence to the asymptotic limit as t→+∞. Finally, in the particular case of a Burgers flux function, we show that the solutions exhibit the phenomenon of metastability.

On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions

Strani M.
2020

Abstract

In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating diffusions (monotone and non monotone) and singular nonlinear diffusions are considered. In particular, the cases of mean curvature-type diffusions both in the Euclidean space and in Lorentz–Minkowski space enter in our framework. After dealing with existence and stability of monotone steady states in a bounded interval of the real line with Dirichlet boundary conditions, we discuss the speed rate of convergence to the asymptotic limit as t→+∞. Finally, in the particular case of a Burgers flux function, we show that the solutions exhibit the phenomenon of metastability.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3722697
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