Stabilization of the transmission Schrodinger equation with boundary time-varying delay

• Published in: International Journal of Applied Mathematics and Simulation Vol. 1; no. 1; pp. 59 - 78
• Main Authors: Moumen, Latifa, Rebiai, Salah-Eddine
• Format: Journal Article
• Language: English
• Published: 19.05.2024
• ISSN: 2992-1708; 2992-1732
• DOI: 10.69717/ijams.v1.i1.95

We consider a system of transmission of the Schrodinger equation with Neumann feedback control that contains a time-varying delay term and that acts on the exterior boundary. Using a suitable energy function and a suitable Lyapunov functional, we prove under appropriate assumptions that the solutions decay exponentially. MSC: 35Q93, 93D15 REFERENCES[1] Allag, I., & Rebiai, S. (2014). Well-posedness, regularity and exact controllability for the problem of transmission of the Schrödinger equation. Quarterly of Applied Mathematics, 72(1), 93-108.‏. Search in Google Scholar   Digital Object Identifier MathSciNet[2] Bayili, G., Aissa, A. B., & Nicaise, S. (2020). Same decay rate of second order evolution equations with or without delay. Systems & Control Letters, 141, 104700.‏. Search in Google Scholar   Digital Object Identifier[3] Cavalcanti, M. M., Corrêa, W. J., Lasiecka, I., & Lefler, C. (2016). 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