TY  - JOUR
ID  - Bégout2026
LB  - Bégout2026
AU  - Bégout, Pascal
AU  - Díaz, Jesús Ildefonso
TI  - Damped nonlinear Ginzburg-Landau equation with saturation. Part II. Strong Stabilization
ST  - Damped nonlinear Ginzburg-Landau equation with saturation. Part II. Strong Stabilization
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 2
SP  - 185
EP  - 199
DO  - https://doi.org/10.7494/OpMath.202603112
UR  - https://doi.org/10.7494/OpMath.202603112
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. As a continuation of our previous study on the existence and uniqueness of solutions, we prove here some strong stabilization properties. In particular, we show the finite time extinction of solutions induced by the nonlinear saturation mechanism, which, sometimes, can be understood as a bang-bang control. The analysis relies on refined energy methods. Our results provide a rigorous justification of nonlinear dissipation as an effective stabilization mechanism for this class of complex equations where the maximum principle fails.
KW  - damped Ginzburg-Landau equation
KW  - saturated nonlinearity
KW  - finite time extinction
SN  - 1232-9274
ER  -