Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity

1991 ◽  
Vol 116 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Reinhard Racke ◽  
Yoshihiro Shibata
Keyword(s):  
Asymptotic Stability ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Nonlinear Thermoelasticity ◽  
Global 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.

Global solutions in one-dimensional magneto-thermoviscoelasticity

1991 ◽  
Vol 2 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Jürgen Sprekels
Keyword(s):  
Electromagnetic Field ◽  
Joule Heating ◽  
Space Variable ◽  
Global Solutions ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Global Smooth Solutions ◽  
Isotropic Solid ◽  
Displacement Currents ◽  
Thermally Conducting

Global smooth solutions are shown to exist for the system governing magneto-thermoviscoelastic phenomena in an electrically and thermally conducting isotropic solid immersed in an electromagnetic field. It is assumed that displacement currents are negligible, and that all field quantities depend on one space variable only; Joule heating is included.

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