Name
Abstract | ||
|---|---|---|
The long-time asymptotics of solutions of the viscous quantum hydrodynamic model in one space dimension is studied. This model consists of continuity equations for the particle density and the current density, coupled to the Poisson equation for the electrostatic potential. The equations are a dispersive and viscous regularization of the Euler equations. It is shown that the solutions converge exponentially fast to the (unique) thermal equilibrium state as the time tends to infinity. For the proof, we employ the entropy dissipation method, applied for the first time to a third-order differential equation. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0893-9659(03)90128-5 | Applied Mathematics Letters |
Keywords | Field | DocType |
Quantum hydrodynamics,Wigner-Fokker-Planck equation,Long-time behavior of solutions,Entropy dissipation method | Fokker–Planck equation,Quantum hydrodynamics,Differential equation,Poisson's equation,Mathematical analysis,Exponential decay,Fluid dynamics,Euler equations,Classical mechanics,Mathematics,Independent equation | Journal |
Volume | Issue | ISSN |
16 | 8 | 0893-9659 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M.P. Gualdani | 1 | 0 | 0.34 |
| A. Jüngel | 2 | 1 | 0.72 |
| Giuseppe Toscani | 3 | 138 | 24.06 |