An initial value problem for a class of higher order partial differential equations related to the heat equation

  • 29 Accesses

  • 5 Citations


  1. [1]

    F. Bernstein,Über das Fourierintegral \(\int\limits_0^\infty {e^{ - x^2 } \cos (tx)dx} \), Math. Annalen,79 (1919), pp. 265–268.

  2. [2]

    G. Birkhoff,Mathematics for engineers. — III:Dimensional analysis of partial differential equations, Electrical Engineering, Dec. 1948.

  3. [3]

    H. Burkill -J. C. Burkill,A second course in mathematical analysis, University Press, Cambridge, 1970.

  4. [4]

    H. S. Carslaw,Introduction to the theory of Fourier's series and integrals, Third Edition, Dover, New York, 1930.

  5. [5]

    H. S. Carslaw - J. C. Jaeger,Conduction of heat in solids, Oxford University Press, 1959.

  6. [6]

    J. Fourier,The analytical theory of heat, translated byA. Freeman, Dover, New York, 1955.

  7. [7]

    E. Goursat,A course in mathematical analysis, Vol. III, Part one, translated byH. G. Bergmann, Dover, New York, 1964.

  8. [8]

    G. Hellwig,Partial differential equations, Blaisdell, New York, 1964.

  9. [9]

    E. W. Hobson,The theory of functions of a real variable and the theory of Fourier's series, Vols. I and II, Dover, New York, 1957.

  10. [10]

    J. Pierpont,The theory of functions of real variables, Vols. I and II, Dover, New York, 1959.

  11. [11]

    R. T. Seeley,An introduction to Fourier series and integrals, W. A. Benjamin, Inc., New York, 1966.

  12. [12]

    E. C. Titchmarsh,Introduction to the theory of Fourier integrals, 2nd Edition, Oxford University Press, London, 1948.

  13. [13]

    A. N. Tychonov, Akad. Nauk SSSR Mat. Sb.,42 (1935), pp. 199–215.

  14. [14]

    A. N. Tychonov -A. A. Samarski,Partial differential equations of mathematical physics, Vol. I, translated byS. Radding, Holden-Day, Inc., San Francisco, 1964.

Download references

Author information

Additional information

Entrato in Redazione il 23 maggio 1972.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Diaz, J.B., Means, C.S. An initial value problem for a class of higher order partial differential equations related to the heat equation. Annali di Matematica 97, 115–187 (1973).

Download citation


  • Differential Equation
  • Partial Differential Equation
  • Heat Equation
  • Order Partial Differential Equation
  • High Order Partial Differential Equation