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21.
Bixiang Wang 《Journal of Mathematical Analysis and Applications》2002,266(1):1-20
This paper deals with the time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions. The uniqueness of global weak solutions is established for this model with initial data of the order parameter in L4 and magnetic potential in L3. 相似文献
22.
Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices
Let Ω⊂R2 be a simply connected domain, let ω be a simply connected subdomain of Ω, and set A=Ω?ω. Suppose that J is the class of complex-valued maps on the annular domain A with degree 1 both on ∂Ω and on ∂ω. We consider the variational problem for the Ginzburg-Landau energy Eλ among all maps in J. Because only the degree of the map is prescribed on the boundary, the set J is not necessarily closed under a weak H1-convergence. We show that the attainability of the minimum of Eλ over J is determined by the value of cap(A)—the H1-capacity of the domain A. In contrast, it is known, that the existence of minimizers of Eλ among the maps with a prescribed Dirichlet boundary data does not depend on this geometric characteristic. When cap(A)?π (A is either subcritical or critical), we show that the global minimizers of Eλ exist for each λ>0 and they are vortexless when λ is large. Assuming that λ→∞, we demonstrate that the minimizers of Eλ converge in H1(A) to an S1-valued harmonic map which we explicitly identify. When cap(A)<π (A is supercritical), we prove that either (i) there is a critical value λ0 such that the global minimizers exist when λ<λ0 and they do not exist when λ>λ0, or (ii) the global minimizers exist for each λ>0. We conjecture that the second case never occurs. Further, for large λ, we establish that the minimizing sequences/minimizers in supercritical domains develop exactly two vortices—a vortex of degree 1 near ∂Ω and a vortex of degree −1 near ∂ω. 相似文献
23.
在文[1]的基础上,得到了二维广义的Ginzburg-Landau方程的指数吸引子的存在性. 相似文献
24.
包立平 《高校应用数学学报(A辑)》2003,18(4):423-430
在空间H1,pg(Ω,Rn)中讨论如下一类变系数Ginzburg-Landau型泛函Eε(Ω)=∫Ωa(x)p|Δu|p+14εpb(x)(|u|2-β2(x))2dx的极小元列的渐近性质.这里2≤p0,m≤a(x),b(x),β(x)≤M,且a(x),b(x),β(x)是光滑函数.研究了当ε→0时极小元的渐近性态,证明了极小元列在H1,pg(Ω,Rn)中强收敛于某个元素,且得到了该元素所满足的微分方程边值问题. 相似文献
25.
张晓轶 《数学物理学报(A辑)》2005,25(5):652-662
该文证明了复Ginzburg Landau方程在非标准的函数空间X_{s,p}中整体解的存在唯一性;考察了其解在X_{0,α+2}中的极限行为,得到当参数ε→0++或a→0, ε→0++时,Ginzburg Landau方程的解关于时间一致收敛到相应极限方程的解 相似文献
26.
The generalized Cahn-Hilliard equation is obtained as the hydrodynamic limit from a stochastic Ginzburg-Landau model. The
associated large-deviation principle is also proved. In the one-dimensional case, we prove a related result about the scaling
limit of conservative Langevin dynamics of an SOS surface. 相似文献
27.
Boling Guo Zhujung Jing Bainian Lu 《Communications in Nonlinear Science & Numerical Simulation》1996,1(4):12-17
The linear dispersive relation of the travelling-wave solution is investigated for cubic G-L equation. Moreover, the relation among the parameter c0, the amplitude |μo| and the most unstable wave number q is discussed. Then convergence of an unconditionally stable, explicit pseudo-spectral scheme is proved by energy estimates. Finally, by using the proposed scheme, the chaotic attractor, bifurcation structure and asymptotic dynamics are obtained. The results show there exist two different types of chaotic attractors for the most unstable wave number qo and was fixed the amplitude |μo| in the same one system. 相似文献
28.
Robert J. Deissler 《Journal of statistical physics》1985,40(3-4):371-395
The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested. 相似文献
29.
Juncheng Wei Matthias Winter 《Proceedings of the American Mathematical Society》2005,133(6):1787-1796
We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling
We classify the existence and stability of all possible standing wave solutions.
We classify the existence and stability of all possible standing wave solutions.
30.
A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force. 相似文献