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Local uniqueness of solutions of the characteristic Cauchy problem

Published online by Cambridge University Press:  09 April 2009

Gerson Petronilho
Affiliation:
Universidade Federal de São Carlos (UFSCar) Departamento de Matem´tica Caixa Postal 67613560 - São Carlos - SP -, Brazil
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Abstract

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Local uniqueness of solutions of the characteristic Cauchy problem is shown for operators which are perturbations of operators which already have such a uniqueness.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bergamasco, A. P. and Ribeiro, H. S., ‘Uniqueness in a doubly characteristic Cauchy problem’, Pacific J. Math. 136 (1989), 229240.Google Scholar
[2]Birkeland, B. and Persson, J., ‘The local Cauchy problem in R2 at a point where two characteristic curves have a common tangent’, J. Differential Equations 30 (1978), 6488.Google Scholar
[3]Menikoff, A., ‘Uniqueness of the Cauchy problem for a classof partial differential equations with double characteristics’, Indiana Univ. Math.J. 25 (1976), 121.CrossRefGoogle Scholar
[4]de Oliveira, O. R. B., ‘Estudo de uma Classe de Operadores Diferenciais Parciais Lineares que se degeneram sobre uma Reta e têm Característica Múltipla fora dela’ Ms. C., Instituto de Matemática e Estatística da Universidade de São Paulo, 1989.Google Scholar
[5]Treves, F., ‘Discrete phenomena in uniqueness in the Cauchy problem’, Proc. Amer. Math. Soc. 46 (1974), 229233.Google Scholar
[6]Treves, F., Linear partial differential equations with constant coefficients: existence, approximation and regularity of solutions, (Math. and its Applications Vol. 6, Gordon and Breach, New York, 1966).Google Scholar