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Limit behavior of global attractors for the complex Ginzburg–Landau equation on infinite lattices

✍ Scribed by Caidi Zhao; Shengfan Zhou

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
265 KB
Volume
21
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this work, the authors first show the existence of global attractors A ε for the following lattice complex Ginzburg-Landau equation:

and A 0 for the following lattice Schrödinger equation:

Then they prove that the solutions of the lattice complex Ginzburg-Landau equation converge to that of the lattice Schrödinger equation as ε → 0+. Also they prove the upper semicontinuity of A ε as ε → 0+ in the sense that lim ε→0+ dist 2 (A ε , A 0 ) = 0.

📜 SIMILAR VOLUMES

On the global existence and small disper
On the global existence and small dispersion limit for a class of complex Ginzburg–Landau equations
✍ Hongjun Gao; Xueqin Wang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 150 KB 👁 1 views

## Abstract In this paper we consider a class of complex Ginzburg–Landau equations. We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial‐value problem in __d__‐dimensional torus 𝕋^__d__^, and that solutions are initially approximated by solutions of t