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Annali di Matematica Pura ed Applicata

, Volume 80, Issue 1, pp 197–214 | Cite as

The cauchy problem for an elliptic parabolic operator

  • D. Sather
  • J. Sather
Article

Summary

Necessary and sufficient conditions are established for the existence of a solution of a Cauchy problem which is not well posed in the sense of Hadamard.

Keywords

Cauchy Problem Parabolic Operator Elliptic Parabolic Operator 
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.

Bibliography

  1. [1]
    N. Aronszajn andK. T. Smith,Theory of Bessel Potentials, Part I, Ann. Inst. Fourier, vol. 11 (1961), pp. 385–475,MathSciNetGoogle Scholar
  2. [2]
    L. Bers,On the continuation of a potential gas flow across the sonic line, Tech. Note 2058, National Advisory Committee for Aeronautics, 1948.Google Scholar
  3. [3]
    F. John,Numerical solution of problems which are not well posed in the sense of Hadamard Symposium on the Numerical Treatment of Partial Differential Equations wiht Real Characteristics, pp. 103–116, Provisional International Computation Centre, Rome, 1959Google Scholar
  4. [4]
    M. M. Lavrentiev,Some Improperly Posed Problems of Mathematical Physics, Springer Verlag. New York, 1967.Google Scholar
  5. [5]
    R. E. A. C. Paley andN. Wiener,Fourier Transforms in the Complex Domain, American Mathematical Society, New York, 1934.Google Scholar
  6. [6]
    L. E. Payne,On some non well posed problems for partial differential equations, Numerical Solutions of Nonlinear Differential Equations, pp. 239–263, Wiley and Sons, New York, 1966.Google Scholar
  7. [7]
    L. E. Payne andD. Sather,On an initial-boundary value problem for a class of degenerate elliptic operators, Ann. Mat Pura Appl., vol. 78 (1968), pp 333–338.MathSciNetGoogle Scholar
  8. [8]
    C. Pucci,Discussione del problema di Cauchy per le equazioni di tipo ellittico, Ann. Mat Pura Appl., Vol. 46 (1958), pp. 131–153.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    E. C. Titchmarsh,Theory of Fourier Integrals, Oxford University Press, 1948.Google Scholar
  10. [10]
    G. N. Watson,Theory of Bessel Functions, Cambridge University Press, 1944.Google Scholar
  11. [11]
    J. M. Zimmerman,Band limited functions and improper boundary value problems for a class of non-linear partial differential equations, J. Math. Mech., vol 11 (1962), pp. 183–196.zbMATHMathSciNetGoogle Scholar
  12. [12]
    K. T. Smith,The Fourier transform of the convolution |x |α-n *g, Tech. Summary Rep. No. 203, Mathematics Research Center, U.S. Army, Univ. of Wisconsin, Madison, Wisc. (1960).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1968

Authors and Affiliations

  • D. Sather
  • J. Sather

There are no affiliations available

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