Abstract
We study the complex Ginzburg–Landau equation posed on possibly unbounded domains, including some singular and saturated nonlinear damping terms. This model interpolates between the nonlinear Schr¨odinger equation and dissipative parabolic dynamics through a complex timederivative prefactor, capturing the interplay between dispersion and dissipation. Under suitable structural conditions on the complex coefficients, we establish the existence and uniqueness of global solutions. The analysis relies on the delicate proofs that the maximal monotone operator theory can be adapted to this framework, even for unbounded domains.
Keywords
Damped Ginzburg–Landau equation,; Saturated nonlinearity,; Finite time extinction,; Maximal monotone operators,; Existence and regularity of weak solutions;
Reference
Pascal Bégout, and Jesus Ildefonso Diaz, “Damped nonlinear Ginzburg–Landau equation with saturation. Part I. Existence of solutions on general domains”, Opuscula Mathematica, vol. 46, n. 2, March 2026, pp. 153–183.
See also
Published in
Opuscula Mathematica, vol. 46, n. 2, March 2026, pp. 153–183