Advertisement

Annali di Matematica Pura ed Applicata

, Volume 94, Issue 1, pp 161–176 | Cite as

On the characteristic initial value problem for the wave equation in odd spatial dimensions with radial initial data

  • J. B. Diaz
  • E. C. Young
Article

Summary

The paper obtains an explicit solution of the characteristic initial value problem for the wave equation in odd spatial dimensions with radial initial data via solution of a characteristic boundary value problem involving a singular differential equation. The solution of the latter problem is obtained by a modified Riemann method. It is shown that on the time axis the solution of the original problem reduces to the solution that is obtainable by the use of Asgeirsson’s mean value theorem.

Keywords

Differential Equation Initial Data Wave Equation Original Problem Spatial Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    R. Courant -D. Hilbert Methods of Mathematical Physics vol. II, Interscience Publishers, New York, 1962.Google Scholar
  2. [2]
    M. Riesz,L’integrale de Riemann-Liouville et le probleme de Cauchy, Acta. Math.,81 (1948), pp. 1–223.CrossRefMathSciNetGoogle Scholar
  3. [3]
    O. G. Owens,Polynomial solutions of the cylindrical wave equation, Duke Math. J.,23 (1956), pp. 371–383.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    L. E. Payne -H. F. Weinberger,Remark on a paper of O. G. Owens, Duke Math. J.,24 (1957), p. 233.CrossRefMathSciNetGoogle Scholar
  5. [5]
    M. H. Protter,The characteristic initial value problem for the wave equation and Riemann’s method, Amer. Math. Monthly,61 (1954), pp. 702–705.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    E. C. Young,The characteristic initial value problem for the wave equation in n-dimensions, J. Math. and Mech.,17 (1968), pp. 885–890.zbMATHMathSciNetGoogle Scholar
  7. [7]
    F. G. Friedlander -A. E. Heins,On a singular boundary value problem for the Euler-Darboux equation, J. Diff. Equa.,4 (1968), pp. 460–491.CrossRefMathSciNetGoogle Scholar
  8. [8]
    A. Weinstein,On the wave equation and Euler-Poisson-Darboux equation, Proc. of the 5th Symposium in Appl. Math., McGraw Hill, New York (1954), pp. 137–147.Google Scholar
  9. [9]
    A. Weinstein,The generalized radiation problem and the Euler-Poisson-Darboux equation, Summa Brasiliensis,3 (1955), pp. 125–146.zbMATHMathSciNetGoogle Scholar
  10. [10]
    J. L. Lions,On the generalized radiation problem of Weinstein, J. Math. Mech.,8 (1959), pp. 873–888.zbMATHMathSciNetGoogle Scholar
  11. [11]
    H. M. Lieberstein,On the generalized radiation problem of A. Weinstein, Pacific J. Math.,7 (1957), pp. 1623–1640.zbMATHMathSciNetGoogle Scholar
  12. [12]
    G. Darboux,Theorie Generale des Surfaces, vol. II, Book 4, Gauthier-Villars, Paris, 1889.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1972

Authors and Affiliations

  • J. B. Diaz
    • 1
  • E. C. Young
    • 1
  1. 1.TallahasseeUSA

Personalised recommendations