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.

ON THE RELAXATION LIMITS OF THE HYDRODYNAMIC MODEL FOR SEMICONDUCTOR DEVICES

2002 ◽  
Vol 12 (03) ◽  
pp. 333-363 ◽  
Author(s):  
YOUCHUN QIU ◽  
KAIJUN ZHANG
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Hydrodynamic Model ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Compensated Compactness ◽  
One Dimensional ◽  
Initial Boundary Value

The initial-boundary value problem of a simplified one-dimensional hydrodynamic model for semiconductors is considered. The global weak solution and its relaxation limit are obtained through using the compensated compactness methods. The traces of weak solutions are also discussed.

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.

scholarly journals On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Gang Li ◽  
Yun Sun ◽  
Wenjun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Nonlinear Viscoelastic ◽  
Petrovsky Equation ◽  
Initial Boundary Value

This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equationutt+Δ2u−∫0tgt−τΔ2ux,τdτ−Δut−Δutt+utm−1ut=up−1u. Under certain conditions ongand the assumption thatm<p, we establish some asymptotic behavior and blow-up results for solutions with positive initial energy.

scholarly journals Operator Approach to the Problem on Small Motions of an Ideal Relaxing Fluid

2018 ◽  
Vol 64 (3) ◽  
pp. 459-489
Author(s):  
D A Zakora
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Basis Property ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Zero Gravity ◽  
Operator Approach ◽  
Special System ◽  
Strong Solvability ◽  
Initial Boundary Value

In this paper, we study the problem on small motions of an ideal relaxing fluid that fills a uniformly rotating or fixed container. We prove a theorem on uniform strong solvability of the corresponding initial-boundary value problem. In the case where the system does not rotate, we find an asymptotic behavior of the solution under the stress of special form. We investigate the spectral problem associated with the system under consideration. We obtain results on localization of the spectrum, on essential and discrete spectrum, and on spectral asymptotics. For nonrotating system in zero-gravity conditions we prove the multiple basis property of a special system of elements. In this case, we find an expansion of the solution of the evolution problem in the special system of elements.

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