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The Convergence Problem for Dissipative Autonomous Systems pp 45–65Cite as

The Linearization Method in Stability Analysis

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Abstract

The most classical way to study asymptotics of a semi-linear evolution equation is the linearization around equilibrium solutions. This enables both asymptotic stability results (Liapunov’s first method) and instability results, the main issue being the nature of eigenvalues of the generator for the linearized equation. Examples in the case of PDE equations are provided for both situations.

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References

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598, 4, place Jussieu, 75005, Paris, France

    Alain Haraux

  2. Institut Préparatoire aux Etudes Scientifiques et Techniques, Université de Carthage, B.P. 51, 2070, La Marsa, Tunisia

    Mohamed Ali Jendoubi

  3. Faculté des sciences de Tunis, Laboratoire EDP-LR03ES04, Université de Tunis El Manar, Tunis, Tunisia

    Mohamed Ali Jendoubi

Authors
  1. Alain Haraux
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  2. Mohamed Ali Jendoubi
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Correspondence to Alain Haraux .

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Haraux, A., Jendoubi, M. (2015). The Linearization Method in Stability Analysis. In: The Convergence Problem for Dissipative Autonomous Systems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-23407-6_6

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