We give a counterexample which shows that the asymptotic rate of convergence to the equilibrium state for the transport equation, with a degenerate cross section and in the periodic setting, cannot be better than t^−1/2 in the general case. We suggest, moreover, that the geometrical properties of the cross section are the key feature of the problem and impose, through the distribution of the forward exit time, the speed of convergence to the stationary state.
On the convergence to equilibrium for degenerate transport problems
SALVARANI, FRANCESCO
2013-01-01
Abstract
We give a counterexample which shows that the asymptotic rate of convergence to the equilibrium state for the transport equation, with a degenerate cross section and in the periodic setting, cannot be better than t^−1/2 in the general case. We suggest, moreover, that the geometrical properties of the cross section are the key feature of the problem and impose, through the distribution of the forward exit time, the speed of convergence to the stationary state.File in questo prodotto:
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