Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains I: The diffeomorphism case
Year: 2016
Type: article
Abstract: The purpose of this article is to analyze the dynamics of the following complex Ginzburg-Landau equation\begin{align*}\partial_{t}u-(\lambda+i\alpha)\Delta u+(\kappa+i\beta)|u|^{p-2}u-\gamma u=f(t)\end{align*}on non-cylindrical domains, which are obtained by diffeomorphic transformation of a bounded base domain, without any upper restriction on $p>2$, only with some restriction on $\beta/\kappa$. We establish the existence and uniqueness of strong and weak solutions as well as some energy inequalities for this equation on variable domains. Moreover the existence of a $\mathscr{D}$-pullback attractor is established for the process generated by the weak solutions under a slightly weaker condition that the measure of the spatial domains in the past is uniformly bounded above.
Authors: Feng Zhou, Chunyou Sun
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2549798694