Infinite memory effects on the stability of Biharmonic Schrödinger equation

2023/01/24 by Roberto de A. Capistrano–Filho, Filho, Roberto de A. Capistrano, Isadora Maria de Jesus +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.10310

openalex publication_date 2023/01/24 · openalex created_date 2023/01/27 · openalex updated_date 2026/07/28

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.

Related

• Exponential stability for an infinite memory wave equation with frictional damping and logarithmic nonlinear terms
• Stable determination of the first order perturbation of the biharmonic operator from partial data
• linearized inverse problem for biharmonic operators at high frequencies
• Biharmonic non-linear Schrödinger equation with an unbounded inhomogeneous term
• Stability for an inverse source problem of the damped biharmonic plate equation