Skip to main content

Oscillatory boundary conditions for acoustic wave equations

  • Chapter

Abstract

In the textbook literature on theoretical acoustics, it was traditional to use the Robin boundary condition with the wave equation. But it was recognized that this was not the physically correct boundary condition. “Acoustic Boundary Conditions” (or ABC) were introduced in the monograph by Morse and Ingard [13, p. 263]. The presentation in [13] is not the usual approach to the wave equations, since the authors treat waves having definite frequency. The time dependent version of ABC was first formulated by Tom Beale and Steve Rosencrans [1] in a very interesting and original paper. ABC will be explained in detail in Section 2.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beale, J. T. and Rosencrans, S. I.Acoustic boundary conditionsBull. Amer. Math. Soc.80(1974), 1276–1278.

    Article  MathSciNet  MATH  Google Scholar 

  2. Beale, J. T.Spectral properties of an acoustic boundary conditionIndiana Univ. Math. J.25(1976), 895–917.

    MathSciNet  MATH  Google Scholar 

  3. Beale, J. T.Acoustic scattering from locally reacting surfacesIndiana Univ. Math. J. 26 (1977), 199–222.

    MathSciNet  MATH  Google Scholar 

  4. Binding, P. A. and Browne, P. J.Left definite Sturm-Liouville problems with eigenparameter dependent boundary conditionsDifferential Integral Equations12(1999), 167–182.

    MathSciNet  MATH  Google Scholar 

  5. Binding, P. A. and Browne, P. J.Sturm-Liouville problems with non-separated eigenvalue dependent boundary conditionsProc. Roy. Soc. Edinburgh Sect. A130(2000), 239–247.

    MathSciNet  MATH  Google Scholar 

  6. Binding, P. A., Browne, P. J. and Watson, B. A.Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditionsJ. London Math. Soc.62(2)(2000), 161–182.

    Article  MathSciNet  MATH  Google Scholar 

  7. Binding, P. A., Browne, P. J. and Watson, B. A.Spectral problems for non-linear Sturm-Liouville equations with eigenparameter dependent boundary conditionsCanad. J. Math.52(2000), 248–264.

    MathSciNet  MATH  Google Scholar 

  8. Favini, A., Goldstein, G. R., Goldstein, J. A. and Romanelli, S.The heat equation with generalized Wentzell boundary conditionJ. Evol. Equations2(2002) 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  9. Favini, A., Goldstein, G. R., Goldstein, J. A. and Romanelli, S., to appear.

    Google Scholar 

  10. Goldstein, J. A.Semigroups of Linear Operators and ApplicationsOxford University Press, Oxford, New York, 1985.

    Google Scholar 

  11. GAL, C. G., PhD thesis, in preparation.

    Google Scholar 

  12. KRAMAR, M., MUGNOLO, D. and Nagel, R.Theory and applications of one-sided couplede operator matricesConf. Sem. Matem. Univ. Bari, to appear.

    Google Scholar 

  13. MORSE, P. M. and INGARD, K. U.Theoretical AcousticsMcGraw-Hill. New York, 1968. [[4] MUGNOLO, D.Abstract wave equations with acoustic boundary conditionspreprint.

    Google Scholar 

  14. Wentzell, A. D., On boundary conditions for multidimensional diffusion processes, Theory Prob. and its Appl.4(1959), 164–177.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to the memory of Philippe Bénilan

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this chapter

Cite this chapter

Gal, C.G., Goldstein, G.R., Goldstein, J.A. (2003). Oscillatory boundary conditions for acoustic wave equations. In: Arendt, W., Brézis, H., Pierre, M. (eds) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7924-8_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7924-8_32

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-7107-4

  • Online ISBN: 978-3-0348-7924-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics