The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up...The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.展开更多
Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-depende...Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.展开更多
This paper studies the asymptotic behavior of solutions to the initial boundary value problem for a nonlinear wave equation arising in an elastic waveguide model. It proves that under rather mild conditions on g the r...This paper studies the asymptotic behavior of solutions to the initial boundary value problem for a nonlinear wave equation arising in an elastic waveguide model. It proves that under rather mild conditions on g the related solution semigroup possesses a local attractor.展开更多
基金L.H. is supported in part by the NSFC (10431060) H.L. is supported partially by the NSFC (10431060, 10871134)+1 种基金the Beijing Nova program (2005B48)the NCET support of the Ministry of Education of China, and the Huo Ying Dong Foundation (111033)
文摘The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.
基金supported by the Italian MIUR-PRIN Research Project 2008 "Transizioni di fase,isteresi e scale multiple"
文摘Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.
文摘This paper studies the asymptotic behavior of solutions to the initial boundary value problem for a nonlinear wave equation arising in an elastic waveguide model. It proves that under rather mild conditions on g the related solution semigroup possesses a local attractor.
