Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. (English) Zbl 1391.93171
Summary: We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed-point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C10 | Nonlinear systems in control theory |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 93C20 | Control/observation systems governed by partial differential equations |
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