共查询到20条相似文献,搜索用时 31 毫秒
1.
Global Existence and Asymptotic Behavior of the Solution to 1-D Energy Transport Model for Semiconductors
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In this paper, we study the asymptotic behavior of global smooth solution to the initial boundary problem for the 1-D energy transport model in semiconductor science. We prove that the smooth solution of the problem converges to a stationary solution exponentially fast as t → ∞ when the initial data is a small perturbation of the stationary solution. 相似文献
2.
Li Chen Ling Hsiao Gerald Warnecke 《应用数学学报(英文版)》2007,23(1):9-28
This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity. 相似文献
3.
Asymptotic Behavior for Global Smooth Solution to a One-dimensional Nonlinear Thermoviscoelastic System
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Yuming Qin 《偏微分方程(英文版)》1999,12(2):111-134
This paper is concerned with asymptotic behavior, as time tends to infinity, of globally defined smooth (large) solutions to the system in one-dimensional nonlinear thermoviscoelasticity. Our results show that the global smooth solution approaches to the solution in the H¹ norm to the corresponding stationary problem, as time tends to infinity. 相似文献
4.
Ling Hsiao Qiangchang Ju Shu Wang 《Mathematical Methods in the Applied Sciences》2003,26(14):1187-1210
We establish the global existence of smooth solutions to the Cauchy problem for the multi‐dimensional hydrodynamic model for semiconductors, provided that the initial data are perturbations of a given stationary solutions, and prove that the resulting evolutionary solution converges asymptotically in time to the stationary solution exponentially fast. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
5.
陈恕行 《中国科学A辑(英文版)》2002,45(8):1012-1019
The stability of the weak planar oblique shock front with respect to the perturbation of the wall is discussed. By the analysis
of the formation and the global construction of shock and its asymptotic behaviour for stationary supersonic flow along a
smooth rigid wall we obtain the stability of the solution containing a weak planar shock front. The stability can be used
to single out a physically reasonable solution together with the entropy condition 相似文献
6.
Giuseppe Da PratoArnaud Debussche 《Journal of Functional Analysis》2002,196(1):180-210
We study the two-dimensional Navier-Stokes equations with periodic boundary conditions perturbed by a space-time white noise. It is shown that, although the solution is not expected to be smooth, the nonlinear term can be defined without changing the equation. We first construct a stationary martingale solution.Then, we prove that, for almost every initial data with respect to a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense. 相似文献
7.
C. Surulescu 《Applicable analysis》2013,92(2):149-165
We study the stationary problem of a viscous, incompressible Navier-Stokes fluid flowing through a flexible tube with thickness. The behavior of the elastic walls of the tube is described by the equations of nonlinear elasticity for a St.Venant-Kirchhoff material. For smooth enough applied exterior forces we prove the existence of a solution to the coupled problem. 相似文献
8.
Yeping Li 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(4):1125-1144
In this paper, we present a bipolar hydrodynamic model from semiconductor devices and plasmas, which takes the form of bipolar isentropic Euler–Poisson with electric field and frictional damping added to the momentum equations. We firstly prove the existence of the stationary solutions. Next, we present the global existence and the asymptotic behavior of smooth solutions to the initial boundary value problem for a one-dimensional case in a bounded domain. The result is shown by an elementary energy method. Compared with the corresponding initial data case, we find that the asymptotic state is the stationary solution. 相似文献
9.
Yuri N. Skiba 《Journal of Mathematical Analysis and Applications》2012,388(1):627-644
Orthogonal projectors and fractional derivatives on a two-dimensional unit sphere are introduced. Hilbert and Banach spaces of smooth functions on the sphere and some embedding assertions are given. The unique solvability of a nonstationary problem of vortex dynamics of viscous incompressible fluid on a rotating sphere is shown. The existence of a weak solution to stationary problem is proved too, and a condition guaranteeing the uniqueness of solution is also given. 相似文献
10.
In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions(close to equilibrium)of the problem converge to the unique stationary solution. 相似文献
11.
In this paper, we study asymptotic behaviour of the global smooth solutions to the multidimensional hydrodynamic model for semiconductors. We prove that the solution of the problem converges to a stationary solution time asymptotically exponentially fast. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary. A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable. 相似文献
13.
14.
In the simplest case of a linearly degenerate mobility, we view the thin-film equation as a classical free boundary problem. Our focus is on the regularity of solutions and of their free boundary in the “complete wetting” regime, which prescribes zero slope at the free boundary. In order to rule out of the analysis possible changes in the topology of the positivity set, we zoom into the free boundary by looking at perturbations of the stationary solution. Our strategy is based on a priori energy-type estimates which provide “minimal” conditions on the initial datum under which a unique global solution exists. In fact, this solution turns out to be smooth for positive times and to converge to the stationary solution for large times. As a consequence, we obtain smoothness and large-time behavior of the free boundary. 相似文献
15.
The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity. 相似文献
16.
The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assumption on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit. 相似文献
17.
The goal of this paper is to investigate the bifurcation properties of stationary points of a class of planar piecewise smooth systems with 3 parameters using the theory of differential inclusions. We especially study the existence of the stationary points on the line of discontinuity of this kind of planar piecewise smooth system. 相似文献
18.
N. D. Zolotareva E. S. Nikolaev 《Computational Mathematics and Mathematical Physics》2016,56(5):764-782
An iterative process implementing an adaptive hp-version of the finite element method (FEM) previously proposed by the authors for the approximate solution of boundary value problems for the stationary reaction–diffusion equation is described. The method relies on piecewise polynomial basis functions and makes use of an adaptive strategy for constructing a sequence of finite-dimensional subspaces based on the computation of correction indicators. Singularly perturbed boundary value test problems with smooth and not very smooth solutions are used to analyze the efficiency of the method in the situation when an approximate solution has to be found with high accuracy. The convergence of the approximate solution to the exact one is investigated depending on the value of the small parameter multiplying the highest derivative, on the family of basis functions and the quadrature formulas used, and on the internal parameters of the method. The method is compared with an adaptive h-version of FEM that also relies on correction indicators and with its nonadaptive variant based on the bisection of grid intervals. 相似文献
19.
Each solution of infinite order of the stationary Schrödinger equation defined in a smooth cone and continuous in the closure can be represented in terms of the modified Poisson integral and an infinite series vanishing continuously on the boundary. 相似文献
20.
A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied. A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is considered. The existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is studied. An efficient algorithm for constructing the point itself a... 相似文献