19
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Condition Is Not sufficient for uniqueness in the cauchy problem

&
Pages 2113-2128 | Published online: 18 Nov 2011

References

  • Alinhac , S. 1983 . Non-unicité du prolème de Cauchy . Ann. of Math. , 117 : 77 – 108 .
  • Alinhac , S. and Zuily , C. 1981 . Unicité et non unicité du problème de Cauchy pour des opérateurs hyperboliques à caractéristiques doubles . Comm. Partial Differential Equations , 7 : 799 – 828 .
  • Calderón , A.P. 1958 . Uniqueness in the Cauchy problem for partial differential equations . Amer. J. Math , 80 : 16 – 36 .
  • Calderón , A.P. 1962 . “ Existence and uniqueness theorems for systems of partial differential equations,in Fluid Dynamics and Applied Mathematics ” . In Proc. Symp. Univ. of Maryland , 147 – 195 . New York : Gordon and Breach . 1961
  • Cohen , P. 1960 . The non-uniqueness of the Cauchy problem . O.N.R.Techn. Report 93 . 1960 , Standford.
  • Colombini , F. , Del Santo , D. and Zuily , C. 1993 . Uniqueness and non-uniqueness in the Cauchy problem for degenerate elliptic operators . Amer.J.Math , 115 1281 – 1297 .
  • Hörmander , L. 1963 . Linear Partial Differential Operators , Berlin : Springer-Verlag .
  • Hörmander , L. 1975 . Non-uniqueness for the Cauchy problem . Springer Lecture Notes in Math , 459 : 36 – 72 .
  • 1983 . The Analysis of Linear Partial Differential Operators , Vol. I-IV , Berlin : Springer-Verlag . 1985
  • Nakane , S. 1984 . Uniqueness and non-uniqueness in the Cauchy problem for a class of operators of degenerate type . J. Differential Eq. , 51 : 78 – 96 .
  • Nirenberg , L. 1972 . “ Lectures on linear partial differential equations ” . In Regional Conf. Ser. in Math. , Vol. 17 , Providence : Amer. Math. Soc. .
  • Nirenberg , L. and Treves , F. 1970 . On local solvability of partial differential equations part I:necessary conditions,part II:sufficient conditions, correction . Comm. Pure Appl. Math. , 23 : 1 – 38 . 24, (1971), 279-288
  • Roberts , G. 1980 . Uniqueness in the Cauchy problem for characteristic operators of Fuchsian type . J. Differential Eq. , 38 : 374 – 392 .
  • Saint Raymond , X. 1986 . L'unicité pour les problèmes de Cauchy linéaires du premier ordre . L'Ens. Math. , 32 : 1 – 55 .
  • Strauss , M. and Treves , F. 1974 . First order linear P.D.E.'s and uniqueness of the Cauchy problem . J. Differential Eq. , 15 : 195 – 209 .
  • Zuily , C. 1983 . “ Uniqueness and non-uniqueness in the Cauchy problem ” . In Progress in Math. , Vol. 33 , Boston : Birkhäuser .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.