scholarly journals Global existence and asymptotic behaviour of the solution to the system in one-dimensional nonlinear thermoviscoelasticity

2001 ◽  
Vol 59 (1) ◽  
pp. 113-142 ◽  
Author(s):  
Yuming Qin
Keyword(s):  
Global Existence ◽  
Asymptotic Behaviour ◽  
One Dimensional ◽  
Nonlinear Thermoviscoelasticity

Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity

1990 ◽  
Vol 115 (3-4) ◽  
pp. 257-274 ◽  
Author(s):  
Song Jiang
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Nonlinear Thermoelasticity ◽  
Initial Boundary Value ◽  
Smooth Data

SynopsisWe consider the initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity in ℝ+; and prove a global existence-uniqueness theorem for small smooth data. The asymptotic behaviour is simultaneously obtained.

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

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