scholarly journals Long Time Decay Rate to a Bipolar Quantum Drift-Diffusion Model

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Yingjie Zhu ◽  
Bo Liang ◽  
Xiting Peng
Keyword(s):  
Decay Rate ◽  
Dimensional Space ◽  
Functional Method ◽  
Time Behavior ◽  
Drift Diffusion Model ◽  
One Dimensional ◽  
Entropy Functional ◽  
Long Time ◽  
Quantum Hydrodynamic ◽  
Time Decay Rate

This paper is devoted to studying the long time behavior of solutions to a bipolar quantum hydrodynamic in one-dimensional space for general pressure functions. The model is usually applied to simulate some quantum effects in semiconductor devices. The decay rate for time variable is obtained by the entropy functional method and semidiscrete technique.

Long-time behavior for the full one-dimensional Frémond model for shape memory alloys

2000 ◽  
Vol 12 (6) ◽  
pp. 423-433 ◽  
Author(s):  
Pierluigi Colli ◽  
Philippe Laurençot ◽  
Ulisse Stefanelli
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Time Behavior ◽  
Long Time Behavior ◽  
One Dimensional ◽  
Long Time

scholarly journals Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis–haptotaxis

2019 ◽  
Vol 29 (07) ◽  
pp. 1387-1412 ◽  
Author(s):  
Peter Y. H. Pang ◽  
Yifu Wang
Keyword(s):  
Tumor Angiogenesis ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
System Of Differential Equations ◽  
One Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
The One ◽  
Global Boundedness ◽  
Angiogenesis Model

This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain [Formula: see text] ([Formula: see text]): [Formula: see text] where [Formula: see text] and [Formula: see text] are positive parameters. For any reasonably regular initial data [Formula: see text], we prove the global boundedness ([Formula: see text]-norm) of [Formula: see text] via an iterative method. Furthermore, we investigate the long-time behavior of solutions to the above system under an additional mild condition, and improve previously known results. In particular, in the one-dimensional case, we show that the solution [Formula: see text] converges to [Formula: see text] with an explicit exponential rate as time tends to infinity.

Initial Value Problems in Viscoelasticity

1988 ◽  
Vol 41 (10) ◽  
pp. 371-378 ◽  
Author(s):  
W. J. Hrusa ◽  
J. A. Nohel ◽  
M. Renardy
Keyword(s):  
Classical Solutions ◽  
Linear Wave ◽  
Time Behavior ◽  
Initial Value ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
Linear Wave Propagation ◽  
Long Time ◽  
Nonlinear Viscoelastic Materials ◽  
Time Existence

We review some recent mathematical results concerning integrodiff erential equations that model the motion of one-dimensional nonlinear viscoelastic materials. In particular, we discuss global (in time) existence and long-time behavior of classical solutions, as well as the formation of singularities in finite time from smooth initial data. Although the mathematical theory is comparatively incomplete, we make some remarks concerning the existence of weak solutions (i e, solutions with shocks). Some relevant results from linear wave propagation will also be discussed.

FROM BOUNDARY VALUE PROBLEMS TO DIFFERENCE EQUATIONS: A METHOD OF INVESTIGATION OF CHAOTIC VIBRATIONS

1999 ◽  
Vol 09 (07) ◽  
pp. 1285-1306 ◽  
Author(s):  
E. YU. ROMANENKO ◽  
A. N. SHARKOVSKY
Keyword(s):  
Difference Equation ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Dynamical Behavior ◽  
Time Behavior ◽  
One Dimensional ◽  
Long Time ◽  
The Difference ◽  
The One

Among evolutionary boundary value problems for partial differential equations, there is a wide class of problems reducible to difference, differential-difference and other relevant equations. Of especial promise for investigation are problems that reduce to difference equations with continuous argument. Such problems, even in their simplest form, may exhibit solutions with extremely complicated long-time behavior to the extent of possessing evolutions that are indistinguishable from random ones when time is large. It is owing to the reduction to a difference equation followed by the employment of the properties of the one-dimensional map associated with the difference equation, that, it is in many cases possible to establish mathematical mechanisms for one or other type of dynamical behavior of solutions. The paper presents the overall picture in the study of boundary value problems reducible to difference equations (on which the authors have a direct bearing over the last ten years) and demonstrates with several simplest examples the potentialities that such a reduction opens up.

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