Exponential stability for the defocusing semilinear Schrödinger equation with locally distributed damping on a bounded domain. (English) Zbl 1449.35045

Bortot, César Augusto; Corrêa, Wellington José

Differ. Integral Equ. 31, No. 3-4, 273-300 (2018).

Summary: In this paper, we study the exponential stability for the semilinear defocusing Schrödinger equation with locally distributed damping on a bounded domain \(\Omega\subset\mathbb{R}^n\) with smooth boundary \(\partial\Omega\). The proofs are based on a result of unique continuation property due to M. M. Cavalcanti et al. [Differ. Integral Equ. 22, No. 7–8, 617–636 (2009; Zbl 1240.35509)] and on a forced smoothing effect due to L. Aloui [Asymptotic Anal. 59, No. 3–4, 179–193 (2008; Zbl 1173.35392)] combined with ideas from M. M. Cavalcanti et. al. [loc. cit.; J. Differ. Equations 248, No. 12, 2955–2971 (2010; Zbl 1190.35206)] adapted to the present context.

MSC:

35B35	Stability in context of PDEs
35Q55	NLS equations (nonlinear Schrödinger equations)

Keywords:

decay rate estimate; undamped semilinear problem

Citations:

Zbl 1240.35509; Zbl 1173.35392; Zbl 1190.35206