Some stability results for the complex Ginzburg-Landau equation

2018/09/28 by Correia, Simão, Figueira, Mário
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.10913

Abstract

Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg-Landau equation (CGL), ∂_t u = (a + iα) Δu - (b + i β) |u|^σu + k u, t gt; 0, x∈ Ω, with a>0, α, b, β, k ∈ ℝ, are obtained. Moreover, we show the existence of bound-states under certain conditions on the parameters and on the domain. We conclude with the proof of asymptotic stability of these bound-states when Ω=ℝ and -k large enough.

Related

• A generalized Complex Ginzburg-Landau Equation: global existence and\n stability results
• Complex Ginzburg-Landau equations with dynamic boundary conditions
• Local well-posedness of the complex Ginzburg-Landau equation in bounded domains
• Initial-boundary value problems for complex Ginzburg-Landau equations governed by p-Laplacian in general domains
• Periodic Solutions of the complex Ginzburg-Landau Equation in bounded domains