scholarly journals The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors

2003 ◽  
Vol 192 (1) ◽  
pp. 111-133 ◽  
Author(s):  
Ling Hsiao ◽  
Peter A. Markowich ◽  
Shu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Hydrodynamic Model ◽  
Smooth Solutions

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE FULL 1D HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

2002 ◽  
Vol 12 (06) ◽  
pp. 777-796 ◽  
Author(s):  
LING HSIAO ◽  
SHU WANG
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Stationary Solution ◽  
Hydrodynamic Model ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Global Smooth Solutions ◽  
Initial Boundary Value

In this paper, we study the asymptotic behavior of smooth solutions to the initial boundary value problem for the full one-dimensional hydrodynamic model for semiconductors. We prove that the solution to the problem converges to the unique stationary solution time asymptotically exponentially fast.

scholarly journals Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation

2021 ◽  
Author(s):  
Roberta Bianchini ◽  
Roberto Natalini
Keyword(s):  
Asymptotic Behavior ◽  
Boussinesq Equations ◽  
Careful Analysis ◽  
Decay Rates ◽  
Smooth Solutions ◽  
Damping Term ◽  
Bilinear Estimates ◽  
Linearized Problem ◽  
Time Decay Rates ◽  
Velocity Equation

This article deals with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with bilinear estimates and interpolation inequalities for handling the nonlinearity.

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