RANDOM ATTRACTOR FOR FRACTIONAL GINZBURG-LANDAU EQUATION WITH MULTIPLICATIVE NOISE
نویسندگان
چکیده
منابع مشابه
Fractional Ginzburg–Landau equation for fractal media
We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equatio...
متن کاملPsi-series solution of fractional Ginzburg–Landau equation
One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...
متن کاملStochastic Heat Equation with Multiplicative Fractional-Colored Noise
We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...
متن کاملThe Complex Ginzburg-landau Equation∗
Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...
متن کاملDiffusive repair for the Ginzburg-Landau equation
We consider the Ginzburg-Landau equation for a complex scalar field in one dimension and show that small phase and amplitude perturbations of a stationary solution repair diffusively to converge to a stationary solution. Our methods explain the range of validity of the phase equation, and the coupling between the “fast” amplitude equation and the “slow” phase equation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2014
ISSN: 1027-5487
DOI: 10.11650/tjm.18.2014.3053