The Viscous Model of Quantum Hydrodynamics in Several Dimensions
نویسندگان
چکیده
We investigate the viscous model of quantum hydrodynamics in one and higher space dimensions. Exploiting the entropy dissipation method, we prove the exponential stability of the thermal equilibrium state in 1,2, and 3 dimensions, provided that the domain is a box. Further, we show the local in time existence of a solution in the one dimensional case; and in the case of higher dimensions under the assumption of periodic boundary conditions. Finally, we discuss the semiclassical limit.
منابع مشابه
Solutions to the Equations of Viscous Quantum Hydrodynamics in Multiple Dimensions
We study the viscous model of quantum hydrodynamics in a bounded domain of space dimension 1, 2, or 3. This model is a mixed order partial differential system with nonlocal and nonlinear terms for the particle density, current density and electric potential. By a viscous regularization approach, we show existence and uniqueness of local in time solutions. 2000 Mathematics Subject Classification...
متن کاملتوسعه یک روش عددی حجم محدود برای ارزیابی عملکرد هیدرودینامیکی سازه های دریایی
Development of a compatible computational fluid dynamics procedure to investigate rigid and fixed/free coastal and offshore structures hydrodynamics in a time-dependent one/two phase flow of viscous incompressible fluids is presented. Differential governing equations are discretised using finite volume approach based on a colocated arrangement. The conservation equations for mass and momentum a...
متن کاملA Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Single-sided Time Window Setting
Customer service level is of prime importance in today competitive world and has various dimensions with delivery quality being one of the most important ones. Delivery quality has several parameters such as deliver time window options, time window size, etc. In this paper we focus on one of these parameters, namely time window setting. It has a direct impact upon customer satisfaction and busi...
متن کاملCompressive and rarefactive dust-ion acoustic solitary waves in four components quantum plasma with dust-charge variation
Based on quantum hydrodynamics theory (QHD), the propagation of nonlinear quantum dust-ion acoustic (QDIA) solitary waves in a collision-less, unmagnetized four component quantum plasma consisting of electrons, positrons, ions and stationary negatively charged dust grains with dust charge variation is investigated using reductive perturbation method. The charging current to the dust grains ca...
متن کاملViscous Quantum Hydrodynamics and Parameter-Elliptic Systems
The viscous quantum hydrodynamic model derived for semiconductor simulation is studied in this paper. The principal part of the vQHD system constitutes a parameter–elliptic operator provided that boundary conditions satisfying the Shapiro–Lopatinskii criterion are specified. We classify admissible boundary conditions and show that this principal part generates an analytic semigroup, from which ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006