Hiroshima Mathematical Journal

Note on the Cauchy problem for linear hyperbolic partial differential equations with constant coefficients

Kiyoshi Yoshida and Syûji Sakai

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 1, Number 2 (1971), 445-459.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206137984

Digital Object Identifier
doi:10.32917/hmj/1206137984

Mathematical Reviews number (MathSciNet)
MR0310444

Zentralblatt MATH identifier
0265.35052

Subjects
Primary: 35L30: Initial value problems for higher-order hyperbolic equations

Citation

Yoshida, Kiyoshi; Sakai, Syûji. Note on the Cauchy problem for linear hyperbolic partial differential equations with constant coefficients. Hiroshima Math. J. 1 (1971), no. 2, 445--459. doi:10.32917/hmj/1206137984. https://projecteuclid.org/euclid.hmj/1206137984


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References

  • [1] V. M. Borok, Reduction to a single equation of an evolutional system of linear partial differential equations with constant coefficients, Dokl. Akad. Nauk SSSR (N. S.), 114 (1957), 682-685. (In Russian.)
  • [2] A. Friedman, Generalized functions andpartial differential equations, Prentice-Hall, 1963.
  • [3] L. Hormander, Linear partial differentialoperators, Springer, 1969.
  • [4] M. Itano, On a trace theorem for the space H^(RN), J. Sci. Hiroshima Univ. Ser. A-l, 30 (1966), 11-29.
  • [5] M. Itano, On the fine Cauchy problem for the system of linear partial differential equations, J. Sci. HiroshimaUniv. Ser. A-l, 33 (1969), 11-27.
  • [6] M. Itano, Note on the canonical extensions and the boundary values for distributions in the space H, to appear in Hiroshima Math. J..
  • [7] M. Itano, and K. Yoshida, Energy inequalities and Cauchy problems for a system of linear partial differential equations, Hiroshima Math. J., 1(1971), 75-108.
  • [8] J. Kopicek and M. Sucha, The Cauchy problem for weakly hyperbolic systems of linear differential equations with Constant coefficients, Gasopis Pest. Mat., 91 (1966), 431-452. (In Russian.)
  • [9] G. Peyser, Energy inequalities for hyperbolic equations in several variables with multiple characteristics and constant coefficients, Trans. Amer. Math. Soc, 108 (1963), 478-490.
  • [10] S. L. Svensson, Necessary and sufficient conditions for the hyperbolicityof polynomials with hyperbolic principal part, Ark. Math., 8 (1970), 145-162.