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Preprint 2021-03

Marcelo Cavalcanti, Valeria Domingos Cavalcanti, Aissa Guesmia, Mauricio Sepúlveda:

Well-posedness and stability for Schrödinger equations with infinite memory

Abstract:

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.

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