ON THE KRAMERS-FOKKER-PLANCK EQUATION WITH DECREASING POTENTIALS IN DIMENSION ONE

Radek Novak (1) , Xue Ping Wang (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Equations aux dérivées partielles

For quickly decreasing potentials with one position variable, the first threshold zero is always a resonance of the Kramers-Fokker-Planck operator. In this article we study low-energy spectral properties of the operator and calculate large time asymptotics of solutions in terms of the Maxwellian.

Mots clés: Kramers-Fokker-Planck equation; return to local equilibrium; threshold spectral analysis; pseudo-spectral estimates

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Radek Novak, Xue Ping Wang. ON THE KRAMERS-FOKKER-PLANCK EQUATION WITH DECREASING POTENTIALS IN DIMENSION ONE. 2017. ⟨hal-01654733⟩