ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

1IntroductionInthispaper,weintendtostudytheexistenceoftheglobalattractorforthefollowinginitialvalueproblemofGinzburgLandauequationcoupledwithBBMequationinanunboundeddomainR=(-oo,oo)wheree(x,f)isacomplexfunction,n(x,t)isarealscalarfunction,pty,6,T,cr1,a2,P1,P2arerealcoustants,andg1(x),g2(x)aregivenrealfunctions.ThisproblemdescribesthenonlinearinteractionsbetweentheLangnluirwaveandtheionacousticwaveinplasmaphysics,E(z,t)denoteselectricfield,n(x,t)betheperturbationofdensity(see[2,12,6l).In[7]…     

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

1 IntroductionPattern formation in a thin layer of fluid heated from below or above is one of the classicalexamples of weakly non-linear phenomena, where the system evolution is described in terms ofa narrow band of linearly unstable modes. The case of a fluid layer confined between poorlyconduction boundaries leads to a situation in which the critical wavelength for the onset ofconvection diverges, as the vatio of diffusivities of the fluid to boundaries increases. The effectappears both in b…     

Ginzburg-Landau-BBM方程的指数吸引子

本文利用挤压性质和算子分解方法证明了Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－ＢＢＭ耦合方程组周期初边值问题指数吸引子的存在性．     

EXPONENTIAL ATTRACTORS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

1. IntroductionThe infinite dimensional dynamical systems which are defined by nonlinear evolutionequations have a lot of properties sindlar to what the differential dynamical system8 havehad, such as attractor and inertia1 manifold. However, because of spectral barriers and spec-tra1 gap conditions, for many dissipative evolution equations such as the 2D Navior-Stokesequations, the existence of an inertial manifOld still remains to be a precarious question. Themajor difference between inert…     

Homoclinic Bifurcation for Boussinesq Equation with Even Constraint

The exact homoclinic orbits and periodic soliton solution for the Boussinesq equation are shown. The equilibrium solution u0 = -1/6 is a unique bifurcation point. The homoclinic orbits and solitons will be interchanged with the solution varying from one side of-1/6 to the other aide. The solution structure can be understood in general.     

SPECTRAL METHODS FOR THE GL-BBM EQUATIONS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｐｅｒｉｏｄｉｃｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｔｈｅｓｙｓｔｅｍｏｆＧｉｎｚｂｕｒｇ ＬａｎｄａｕｅｑｕａｔｉｏｎｓｃｏｕｐｌｅｄｗｉｔｈＢＢＭｅｑｕａｔｉｏｎｓ:ｘ∈Ｒεｔ+ με-(α1+ｉα2 )εｘｘ+ (β1+ｉβ2 ) ｜ε｜2 ε-ｉδｎε=ｇ1(ｘ) ,(1 .1 )ｎｔ+ ｆ(ｎ) ｘ+λｎ-αｎｘｘ-ｎｘｘｔ+ ｜ε｜2 ｘ =ｇ2 (ｘ) ,(1 .2 )ε(ｘ+ 2π ,ｔ) =ε(ｘ ,ｔ) ,ｎ(ｘ + 2π ,ｔ) =ｎ(ｘ ,ｔ) ,(1 .3)ε(ｘ ,0 )…