𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters

✍ Scribed by Alexander Mielke

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
599 KB
Volume
117
Category
Article
ISSN
0167-2789

No coin nor oath required. For personal study only.

✦ Synopsis

The diameter in the L~-norm of the global attractor of the complex Ginzburg-Landau equation ut = (1+lot) Au + Ru -(l+ifl)iul2"u is estimated by using weighted energy estimates for the solutions on the whole space R a. For all parameters d, or, oe, and fl for which global existence is known we obtain the bound Ca(d, or, or, fl)R l/(2~r) . Upper estimates for C~ are given which are polynomial in (c~,/3) for dcr < 2 and exponential for dcr = 2.

📜 SIMILAR VOLUMES

On the stable hole solutions in the comp
On the stable hole solutions in the complex Ginzburg–Landau equation
✍ Orazio Descalzi; Gustavo Düring; Enrique Tirapegui 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 203 KB

We show numerically that the one-dimensional quintic complex Ginzburg-Landau equation admits four different types of stable hole solutions. We present a simple analytic method which permits to calculate the region of existence and approximate shape of stable hole solutions in this equation. The anal

On self-similar singular solutions of th
On self-similar singular solutions of the complex Ginzburg-Landau equation
✍ Petr Plecháč; Vladimír Šverák 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 637 KB

## Abstract We address the open problem of existence of singularities for the complex Ginzburg‐Landau equation. Using a combination of rigorous results and numerical computations, we describe a countable family of self‐similar singularities. Our analysis includes the supercritical nonlinear Schrödi