Well-posedness and stability for Schr\"odinger equations with infinite memory
Analysis of PDEs
2023-01-20 v1
Abstract
We study in this paper the well-posedness and stability for two linear Schr\"odinger equations in -dimensional open bounded domain under Dirichlet boundary conditions with an infinite memory. First, we establish the well-posedness in the sens of semigroup theory. Then, a decay estimate depending on the smoothness of initial data and the arbitrarily growth at infinity of the relaxation function is established for each equation with the help of multipliers method.
Keywords
Cite
@article{arxiv.2102.00331,
title = {Well-posedness and stability for Schr\"odinger equations with infinite memory},
author = {Marcelo Cavalcanti and Valeria Domingos Cavalcanti and Aissa Guesmia and Mauricio Sepúlveda},
journal= {arXiv preprint arXiv:2102.00331},
year = {2023}
}