Nonhomogeneous boundary value problems for the complex Ginzburg–Landau equation posed on a finite interval

Abstract

This paper is concerned with the well-posedness of the complex Ginzburg–Landau equation posed on a finite interval (0, L) with nonhomogeneous Dirichlet boundary conditions. When the initial datum belongs to () and the boundary data belong to some subspace of , the complex Ginzburg–Landau equation is shown to be globally well-posed.

Keywords:

• Ginzburg–Landau equation
• initial boundary value problem
• well-posedness

AMS Subject Classifications:

• 35A01
• 35C15
• 35D30
• 35K20
• 35K55

Acknowledgements

The authors would like to show their deep gratitude to Prof. Bing-Yu Zhang for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11301425], grant number 11571244], [grant number 11231007]; the PCSIRT of the Ministry of Education of China [grant number IRT_16R53].