Exponential stability for the nonlinear Schrödinger equation with locally distributed damping
Küçük Resim Yok
Tarih
2019
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Schrödinger equation, Exponential stability, Locally distributed damping
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Cavalcanti, 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.
