TY  - JOUR
ID  - Bégout2026
LB  - Bégout2026
AU  - Bégout, Pascal
AU  - Díaz, Jesús Ildefonso
TI  - Damped nonlinear Ginzburg-Landau equation with saturation. Part I. Existence of solutions on general domains
ST  - Damped nonlinear Ginzburg-Landau equation with saturation. Part I. Existence of solutions on general domains
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 2
SP  - 153
EP  - 183
DO  - https://doi.org/10.7494/OpMath.202603111
UR  - https://doi.org/10.7494/OpMath.202603111
AB  - 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 Schrödinger equation and dissipative parabolic dynamics through a complex time-derivative 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.
KW  - damped Ginzburg-Landau equation
KW  - saturated nonlinearity
KW  - finite time extinction
KW  - maximal monotone operators
KW  - existence and regularity of weak solutions
SN  - 1232-9274
ER  -