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Stability in Hilbert spaces by using the Riccati equation

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Equadiff 82

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1017))

Abstract

The regulator problem and the operatorial Riccati equation are discussed in Hilbert spaces. The results are then applied in the study of Liapunov stability for some non linear evolution equations.

In particular, we discuss a wave equation with friction coupled with an ordinary differential equation by using some energy functions, which are obtained via the Riccati equation.

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References

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Authors and Affiliations

  1. Department of Mathematics, Facultés Universitaires N.-D. de la Paix, B-5000, Namur, Belgium

    J. -Cl. Louis

Authors
  1. J. -Cl. Louis
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Editor information

H. W. Knobloch Klaus Schmitt

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© 1983 Springer-Verlag

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Louis, J.C. (1983). Stability in Hilbert spaces by using the Riccati equation. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103270

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  • DOI: https://doi.org/10.1007/BFb0103270

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

  • eBook Packages: Springer Book Archive

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