TY - JOUR
T1 - On the Convergence to Equilibrium for Degenerate Transport Problems
AU - Bernard, Étienne
AU - Salvarani, Francesco
PY - 2013/6/1
Y1 - 2013/6/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84877077916
U2 - 10.1007/s00205-012-0608-2
DO - 10.1007/s00205-012-0608-2
M3 - Article
AN - SCOPUS:84877077916
SN - 0003-9527
VL - 208
SP - 977
EP - 984
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 3
ER -