A note on the long time behavior for the Drift-Diffusion-Poisson system

Naoufel Ben Abdallah (1) , Florian Méhats (1) , Nicolas Vauchelet (1)

1 MIP - Mathématiques pour l'Industrie et la Physique

In this note we analyze the long time behavior of a drift-diffusion-Poisson system with a symmetric definite positive diffusion matrix, subject to Dirichlet boundary conditions. This system models the transport of electrons in semiconductor or plasma devices. By using a quadratic relative entropy obtained by keeping the lowest order term of the logarithmic relative entropy, we prove the exponential convergence to the equilibrium.

Domaines: Equations aux dérivées partielles [math.AP]

Naoufel Ben Abdallah, Florian Méhats, Nicolas Vauchelet. A note on the long time behavior for the Drift-Diffusion-Poisson system. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339, pp.683-688. ⟨10.1016/j.crma.2004.09.025⟩. ⟨hal-00378933⟩