Infinite memory effects on the stability of Biharmonic Schr\"odinger equation

TL;DR

This paper investigates how infinite memory damping affects the stability of the Biharmonic Schrödinger equation, showing solutions decay polynomially over time depending on initial data smoothness and kernel growth.

Contribution

It introduces a stability analysis for the Biharmonic Schrödinger equation with infinite memory damping, revealing decay rates influenced by kernel properties and initial data smoothness.

Findings

Solutions decay at a polynomial rate like t^{-n}

Decay rate depends on kernel growth at infinity

Stability results depend on initial data smoothness

Abstract

This paper deals with the stabilization of the linear Biharmonic Schr\"odinger 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.