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UID:20250716T212932EDT-5943z6uPPo@132.216.98.100
DTSTAMP:20250717T012932Z
DESCRIPTION:Title:Stationary solutions to the hydrodynamic model of semicon
 ductors\n\nAbstract:\n\nThe hydrodynamic model of semiconductors is actual
 ly a compressible Euler-Poisson system with relaxation. It describes the t
 ransport of electrons or holes in semiconductor devices. In our recent pro
 ject\, we aim to clarify the whole dynamics of this hydrodynamic model. At
  the first step\, we focus on the classification of its stationary solutio
 ns with appropriate boundary conditions in 1 D (here we choose sonic bound
 ary condition). Mathematically\, the sonic boundary condition is equivalen
 t to the degeneracy of the system at boundary\, which makes the project in
 teresting and also challenging. We find that the structure of the solution
 s depends on the positions of doping profile and the strength of relaxatio
 n. More precisely\, we show that\, when the doping profile is subsonic\, t
 he steady-state equations possess a unique interior subsonic solution\, an
 d at least one interior supersonic solution\; and if further the relaxatio
 n time is large\, then the equations admit infinitely many interior transo
 nic solutions of shock type\; while if the relaxation time is small\, then
  the system has no transonic solutions of shock type but has infinitely ma
 ny smooth transonic solutions. When the doping profile is supersonic\, the
  system does not hold any subsonic solution\; furthermore\, it doesn't adm
 it any supersonic solution or any transonic solution if the supersonic dop
 ing profile is small or the relaxation time is small\, but it has at least
  one supersonic solution and infinitely many transonic solutions if the do
 ping profile is close to the sonic line and the relaxation time is large. 
 This explains the physical phenomenon that pure semiconductor device does 
 not work well. We also study the asymptotic stability of the steady subson
 ic solutions under suitable initial-boundary-value conditions\, by overcom
 ing the non-flatness of the solutions and the degeneracy with different st
 rength at two boundary points.\n
DTSTART:20181029T200000Z
DTEND:20181029T210000Z
LOCATION:Room 1140\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Jingyu Li (Northeast Normal University)
URL:/mathstat/channels/event/jingyu-li-northeast-norma
 l-university-290697
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