Global Carleman Estimate and State Observation Problem for Ginzburg-Landau Equation
Fangfang Dou, Zhonghua Liao, Xiaomin Zhu
TL;DR
This paper establishes a global Carleman estimate for the complex Ginzburg-Landau operator with nonlinear terms and applies it to solve state observation problems, advancing control theory for complex PDEs.
Contribution
It introduces a novel global Carleman estimate for the nonlinear Ginzburg-Landau operator and applies it to state observation problems.
Findings
Proved a global Carleman estimate for the Ginzburg-Landau operator.
Applied the estimate to solve state observation problems.
Enhanced understanding of control for complex nonlinear PDEs.
Abstract
In this paper, we prove a global Carleman estimate for the complex Ginzburg- Landau operator with a cubic nonlinear term in a bounded domain of Rn, n = 2, 3. As applications, we study state observation problems for the Ginzburg-Landau equation.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · advanced mathematical theories · Stability and Controllability of Differential Equations