Electron. J. Differential Equations, Vol. 2017 (2017), No. 129, pp. 1-14.

Memory boundary feedback stabilization for Schrodinger equations with variable coefficients

Abdesselam Nawel, Khaled Melkemi

First we consider the boundary stabilization of Schrodinger equations with constant coefficient memory feedback. This is done by using Riemannian geometry methods and the multipliers technique. Then we explore the stabilization limits of Schrodinger equations whose elliptical part has a variable coefficient. We established the exponential decay of solutions using the multipliers techniques. The introduction of dissipative boundary conditions of memory type allowed us to obtain an accurate estimate on the uniform rate of decay of the energy for Schrodinger equations.

Submitted February 20, 2017. Published May 11, 2017.
Math Subject Classifications: 93D15, 35J10, 35B40, 53C17.
Key Words: Schrodinger equation; exponential stabilization; boundary condition of memory type; Riemannian geometry.

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Abdesselam Nawel
Department of Mathematics
University of Laghouat, Algeria
email: nawelabedess@gmail.com
  Khaled Melkemi
Department of Mathematics
University of Batna II, Algeria
email: k.melkemi@univ-batna2.dz

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