Global Smooth Solutions to the Initial-Boundary Value Problem for the Equations of One-Dimensional Nonlinear Thermoviscoelasticity

1982 ◽  
Vol 13 (3) ◽  
pp. 397-408 ◽  
Author(s):  
C. M. Dafermos
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Global Smooth Solutions ◽  
Nonlinear Thermoviscoelasticity ◽  
Initial Boundary Value

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 Formulation and analysis of a parabolic transmission problem on disjoint intervals

2012 ◽  
Vol 91 (105) ◽  
pp. 111-123 ◽  
Author(s):  
Bosko Jovanovic ◽  
Lubin Vulkov
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Input Data ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Initial Boundary Value

We investigate an initial-boundary-value problem for one dimensional parabolic equations in disjoint intervals. Under some natural assumptions on the input data we proved the well-posedness of the problem. Nonnegativity and energy stability of its weak solutions are also studied.

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