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Exponential Stabilization for the Nonlinear Schrödinger Equation with Localized Damping

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Abstract

Results of exponential stability related to the nonlinear Schrödinger equation posed on the whole real line will be discussed in this paper. We shall use local smoothing effect associated with the semigroup of the Schrödinger equation, Strichartz estimates, and compactness tools to determine the exponential decay of the energy, by assuming the initial data in convenient bounded sets of L 2.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo, 5790, CEP 87020-900, Maringá, PR, Brazil

    Fábio Natali

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  1. Fábio Natali
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Correspondence to Fábio Natali.

Additional information

Research of F. Natali partially supported by the CNPq/Brazil.

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Natali, F. Exponential Stabilization for the Nonlinear Schrödinger Equation with Localized Damping. J Dyn Control Syst 21, 461–474 (2015). https://doi.org/10.1007/s10883-015-9270-y

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  • DOI: https://doi.org/10.1007/s10883-015-9270-y

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