Marcelo Cavalcanti, Valeria Domingos Cavalcanti, Aissa Guesmia, Mauricio Sepúlveda:
Well-posedness and stability for Schrödinger equations with infinite memory
We study in this paper the well-posedness and stability for two linear Schrödinger equations in $d$-dimensional open bounded domain under Dirichlet boundary conditions with an infinite memory. First, we establish the well-posedness in the sense 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.