Large data solutions to the viscous quantum hydrodynamic model with barrier potential

Global Existence of Solutions to One-dimensional Viscous Quantum Hydrodynamic Equations

The existence of global-in-time weak solutions to the one-dimensional viscous quantum hydrodynamic equations is proved. The model consists of the conservation laws for the particle density and particle current density, including quantum corrections from the Bohm potential and viscous stabilizations arising from quantum Fokker-Planck collision terms in the Wigner equation. The model equations ar...

Exponential decay in time of solutions of the viscous quantum hydrodynamic equations

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 ...

Traveling wave solutions for a quantum hydrodynamic model

A traveling wave analysis for a quantum hydrodynamic model ist performed. The isobaric, isentropic and isothermal cases are studied. In all three cases the qualitative behaviour of the solutions is analysed.

Local Existence of Solutions to the Transient Quantum Hydrodynamic Equations

Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors

We establish the global existence of smooth solutions to the Cauchy problem for the one{dimensional isentropic Euler{Poisson (or hydrodynamic) model for semiconductors for small initial data. In particular we show that, as t ! 1, these solutions converge to the stationary solutions of the drift{diiusion equations. The existence and uniqueness of stationary solutions to the drift-diiusion equati...