Skip to main content

Wave propagation for abstract integrodifferential equations

  • Conference paper
  • First Online:
Infinite-Dimensional Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1076))

  • 513 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barberan, J., I. Herrera: Uniqueness theorems and the speed of propagation of signals in viscoelastic materials, Arch. Rat. Mech. Anal., 23 (1966), 173–190.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bloom, F.: Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory, SIAM, Philadelphia, 1981.

    Book  MATH  Google Scholar 

  3. Davis, P.L.: Hyperbolic integrodifferential equations arising in the electrodynamic theory of dielectrics, J. Diff. Eqs., 18 (1975), 170–178.

    Article  MATH  Google Scholar 

  4. Desch, W., R. Grimmer: Invariance and wave propagation for nonlinear integrodifferential equations in Banach spaces, preprint.

    Google Scholar 

  5. Desch, W., R. Grimmer, W. Schappacher: Some considerations for linear integrodifferential equations, J. Math. Anal. Appl., to appear.

    Google Scholar 

  6. Fattorini, H.O.: The Cauchy Problem, Addison-Wesley, Reading, Mass., 1983.

    MATH  Google Scholar 

  7. Finn, J.M., L.T. Wheeler: Wave propagation aspects of the generalized theory of heat conduction, Z. Angew. Math. Phys., 23 (1972), 927–940.

    Article  MathSciNet  MATH  Google Scholar 

  8. Grimmer, R.: Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc., 273 (1982), 333–349.

    Article  MathSciNet  MATH  Google Scholar 

  9. Grimmer, R.: Resolvents for integral equations in abstract spaces, in "Evolution Equations and Applications", F. Kappel and W. Schappacher (eds.), Research Notes in Math., 101–120, Pitman, London, 1982.

    Google Scholar 

  10. Grimmer, R., M. Zeman: Wave propagation for linear integrodifferential equations, J. Diff. Eqs., to appear.

    Google Scholar 

  11. Grimmer, R., S. Spector, M. Zeman: Symmetric hyperbolic integrodifferential equations, preprint.

    Google Scholar 

  12. Gurtin, M.E., A.C. Pipkin: A general theory of heat conduction with finite wave speeds, Arch. Rat. Mech. Anal., 31 (1968), 113–126.

    Article  MathSciNet  MATH  Google Scholar 

  13. Miller, R.K.: An integrodifferential equation for rigid heat conductors with memory, J. Math. Anal. Appl., 66 (1978), 313–332.

    Article  MathSciNet  MATH  Google Scholar 

  14. Miller, R.K., R.L. Wheeler: A remark on hyperbolic integrodifferential equations, J. Diff. Eqs., 24 (1977), 51–56.

    Article  MathSciNet  MATH  Google Scholar 

  15. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.

    Book  MATH  Google Scholar 

  16. Prüss, J.: On resolvent operators for linear integrodifferential equations of Volterra type, J. Integral Eqs., 5 (1983), 211–236.

    Google Scholar 

  17. Reed, M.: Non-linear Wave Equations, Lecture Notes in Math. v. 507, Springer, Berlin, 1976.

    Book  MATH  Google Scholar 

  18. Tanabe, H.: Equations of Evolution, Pitman, London, 1979.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Franz Kappel Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Desch, G.W., Grimmer, R., Zeman, M. (1984). Wave propagation for abstract integrodifferential equations. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072766

Download citation

  • DOI: https://doi.org/10.1007/BFb0072766

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics