On a coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

1997 ◽  
Vol 38 (5) ◽  
pp. 2465-2474 ◽  
Author(s):  
Jinqiao Duan ◽  
Charles Bu ◽  
Hongjun Gao ◽  
Mario Taboada
Keyword(s):  
Marangoni Convection ◽  
Type Model ◽  
Ginzburg Landau

The existence of multiple solutions for a Ginzburg–Landau type model of superconductivity

1996 ◽  
Vol 7 (6) ◽  
pp. 559-574 ◽  
Author(s):  
S. P. Hastings ◽  
M. K. Kwong ◽  
W. C. Troy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Type Model ◽  
Ginzburg Landau ◽  
Second Order Differential Equations ◽  
Parameter Values ◽  
Superconductor Material

We study a system of two second-order differential equations with cubic nonlinearities which model a film of superconductor material subjected to a tangential magnetic field. We verify some recent conjectures of one of the authors about multiplicity of solutions. We show that for an appropriate range of parameter values the relevant boundary value problem has at least two symmetric solutions. It is also proved that a second range of parameters exists for which there are three symmetric solutions.

scholarly journals Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lei Shi
Keyword(s):  
Asymptotic Behavior ◽  
Bifurcation Analysis ◽  
Trivial Solution ◽  
Type Model ◽  
Bifurcation Parameter ◽  
Local Behavior ◽  
Nontrivial Solutions ◽  
Ginzburg Landau ◽  
The Stability ◽  
Bifurcation And Stability

We study the bifurcation and stability of trivial stationary solution(0,0)of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain(0,L)with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the lengthLof the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.

scholarly journals A Ginzburg–Landau type model of superconducting/normal junctions including Josephson junctions

1995 ◽  
Vol 6 (2) ◽  
pp. 97-114 ◽  
Author(s):  
S. Jonathan Chapman ◽  
Qiang Du ◽  
Max D. Gunzburger
Keyword(s):  
Josephson Junctions ◽  
Flux Pinning ◽  
Computational Experiments ◽  
Type Model ◽  
Computational Simulations ◽  
Ginzburg Landau ◽  
Modified Model ◽  
Landau Model

A model for superconductors co-existing with normal materials is presented. The model, which applies to such situations as superconductors containing normal impurities and superconductor/normal material junctions, is based on a generalization of the Ginsburg–Landau model for superconductivity. After presenting the model, it is shown that it reduces to well-known models due to de Gennes for certain superconducting/normal interfaces, and in particular, for Josephson junctions. A provident feature of the modified model is that it can, by itself, account for all of these as well as other physical situations. The results of some preliminary computational experiments using the model are then provided; these include flux pinning by normal impurities and a superconductor/normal/superconductor junction. A side benefit of the modified model is that, through its use, these computational simulations are more easily obtained.

ENERGY CONCENTRATION PROPERTIES OF A p-GINZBURG–LANDAU MODEL

2021 ◽  
pp. 1-22
Author(s):  
YUTIAN LEI
Keyword(s):  
Decay Rate ◽  
Liouville Theorem ◽  
Finite Energy ◽  
Singularity Analysis ◽  
Energy Concentration ◽  
Energy Estimates ◽  
Type Model ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Concentration Properties

Abstract This paper is concerned with the p-Ginzburg–Landau (p-GL) type model with $p\neq 2$ . First, we obtain global energy estimates and energy concentration properties by the singularity analysis. Next, we give a decay rate of $1-|u_\varepsilon |$ in the domain away from the singularities when $\varepsilon \to 0$ , where $u_\varepsilon $ is a minimizer of p-GL functional with $p \in (1,2)$ . Finally, we obtain a Liouville theorem for the finite energy solutions of the p-GL equation on $\mathbb {R}^2$ .

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