Global solution to a generalized nonisothermal Ginzburg-Landau system

Lower bounds for generalized Ginzburg-Landau functionals

Limits of Solutions to the Generalized Ginzburg-Landau Functional

Here f(u) = (DF )(u) is the negative gradient of F w.r.t. u. Note that weak solutions to (1.2) are smooth for p = 2. It is also well-known that, for p 6= 2, weak solutions u to (1.2) are in C , for some 2 (0; 1) (see also [Tp]). The functional I has been used by Chen-Struwe [CS], where they proved the negative gradient ow of I converges to a global weak solution of the heat equations of harmoni...

Global Existence via Ginzburg-Landau Formalism and Pseudo-Orbits of Ginzburg-Landau Approximations

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the c...

On a Cubic-quintic Ginzburg-landau Equation with Global Coupling

We study standing wave solutions in a parabolic partial diierential equations which consists of a cubic-quintic equation stabilized by global coupling A 2 (y) dy : We classify the existence and stability of all posssible standing wave solutions.

Bifurcation and of the Generalized Complex Ginzburg–landau Equation

We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the tri...