Infinite memory effects on the stabilization of a biharmonic Schrödinger equation

Abstract

This paper deals with the stabilization of the linear biharmonic Schrödinger equation in an $n$-dimensional open bounded domain under Dirichlet–Neumann boundary conditions considering three infinite memory terms as damping mechanisms. We show that depending on the smoothness of initial data and the arbitrary growth at infinity of the kernel function, this class of solution goes to zero with a polynomial decay rate like $t^{-n}$ depending on assumptions about the kernel function associated with the infinite memory terms.

Keywords

• biharmonic schrödinger equation
• well-posedness
• infinite memory
• stabilization