Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-nlvjk Total loading time: 0.314 Render date: 2022-05-20T05:24:20.734Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

Analysis of the viscous quantum hydrodynamic equations for semiconductors

Published online by Cambridge University Press:  04 March 2005

MARIA PIA GUALDINI
Affiliation:
Fachbereich Mathematik und Informatik, Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany email gualdani@mathematik.uni-mainz.de, juengel@mathematik.uni-mainz.de
ANSGAR JÜNGEL
Affiliation:
Fachbereich Mathematik und Informatik, Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany email gualdani@mathematik.uni-mainz.de, juengel@mathematik.uni-mainz.de

Abstract

The steady-state viscous quantum hydrodynamic model in one space dimension is studied. The model consists of the continuity equations for the particle and current densities, coupled to the Poisson equation for the electrostatic potential. The equations are derived from a Wigner–Fokker–Planck model and they contain a third-order quantum correction term and second-order viscous terms. The existence of classical solutions is proved for “weakly supersonic” quantum flows. This means that a smallness condition on the particle velocity is still needed but the bound is allowed to be larger than for classical subsonic flows. Furthermore, the uniqueness of solutions and various asymptotic limits (semiclassical and inviscid limits) are investigated. The proofs are based on a reformulation of the problem as a fourth-order elliptic equation by using an exponential variable transformation.

Type
Papers
Copyright
2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
38
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Analysis of the viscous quantum hydrodynamic equations for semiconductors
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Analysis of the viscous quantum hydrodynamic equations for semiconductors
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Analysis of the viscous quantum hydrodynamic equations for semiconductors
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *