On the linear stability of hyperbolic PDEs and viscoelastic flows

  • Michael Renardy
Original Papers


The issue addressed in this paper is whether linear stability can be determined from the spectrum. We present a counterexample for a hyperbolic PDE in two dimensions and a positive result for parallel shear flows of a class of viscoelastic fluids.


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  1. [1]
    S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math.,17, 35–92 (1964).Google Scholar
  2. [2]
    A. F. Neves, H. de Souza Ribeiro and O. Lopes,On the spectrum of evolution operators generated by hyperbolic systems, J. Func. Anal.,67, 320–344 (1986).Google Scholar
  3. [3]
    J. Prüß, On the spectrum of Co-semigroups, Trans. Amer. Math. Soc.,284, 847–857 (1984).Google Scholar
  4. [4]
    M. Renardy,On the stability of parallel shear flow of an Oldroyd B fluid, Diff. Integral Eq.,6, 481–489 (1993).Google Scholar
  5. [5]
    M. Renardy, On the type of certain Co-semigroups, Comm. Part. Diff. Eq.,18, 1299–1307 (1993).Google Scholar
  6. [6]
    J. Zabczyk, A note on Co-semigroups, Bull. Acad. Polon. Sci., Ser. Sci. Math.,23, 895–898 (1975).Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Michael Renardy
    • 1
  1. 1.Dept of MathematicsVirginia TechBlacksburgUSA

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