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Rayleigh Problem and Friedrichs Model

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Operator Theory and Boundary Eigenvalue Problems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 80))

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Abstract

Study of linear stability for ideal fluid plane-parallel flow leads to Rayleigh equation and associated boundary eigenvalue problem being both singular and non-selfadjoint. Operatortheoretic formulation of this problem is treated within the framework of Friedrichs model. Stationary scattering theory technique is applied to obtain corresponding eigen-function expansion theorem in the case when velocity profile of main stationary flow is close to linear. Besides, inverse scattering problem related to Rayleigh equation is considered. Local solvability of this problem and local uniqueness property are established.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Moscow State University, 119899, Moscow, Russia

    Stanislaw A. Stepin

Authors
  1. Stanislaw A. Stepin
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Institut fĂĽr Analysis, technische Mathematik und Versicherungsmathematik, TU Wien, 1040, Wien, Austria

    H. Langer

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Stepin, S.A. (1995). Rayleigh Problem and Friedrichs Model. In: Gohberg, I., Langer, H. (eds) Operator Theory and Boundary Eigenvalue Problems. Operator Theory: Advances and Applications, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9106-6_15

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  • DOI: https://doi.org/10.1007/978-3-0348-9106-6_15

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9909-3

  • Online ISBN: 978-3-0348-9106-6

  • eBook Packages: Springer Book Archive

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