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arXiv · 2102.00331

Well-posedness and stability for Schr\"odinger equations with infinite memory

Marcelo Cavalcanti·Valeria Domingos Cavalcanti·Aissa Guesmia·Mauricio Sepúlveda
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Abstract

We study in this paper the well-posedness and stability for two linear Schr\"odinger equations in $d$-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.

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Marcelo Cavalcanti, Valeria Domingos Cavalcanti, Aissa Guesmia, Mauricio Sepúlveda. 2021-01-30. Well-posedness and stability for Schr\"odinger equations with infinite memory. https://doi.org/10.1007/s00245-022-09864-1

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