Exponential stability for the nonlinear Schrödinger equation with locally distributed damping
AuthorCavalcanti, Marcelo M.
Correa, Wellington J.
Vejar Asem, Rodrigo
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CitationCavalcanti, M. M., Correa, W. J., Özsarı, T., Sepulveda, M., Vejar Asem, R. (2019). Exponential stability for the nonlinear Schrödinger equation with locally distributed damping. International Conference of Mathematical Sciences (ICMS 2019). s. 6.
This talk is concerned with the defocusing nonlinear Schr¨odinger equation with a locally distributed damping on a smooth bounded domain. We first construct approximate solutions for this model by using the theory of monotone operators. We show that these approximate solutions decay exponentially fast in the L 2 -sense by using the multiplier technique and a unique continuation property. Then, we prove the global existence as well as the L 2 -decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively. Finally, we implement a precise and efficient algorithm for studying the exponential decay established in the first part of the paper numerically. Our simulations illustrate the efficacy of the proposed control design.
SourceInternational Conference of Mathematical Sciences (ICMS 2019)
- Makale Koleksiyonu 
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