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On the well-posedness of a $ C\sp \infty$ Goursat problem for a partial differential operator of order greater than two


Author: Jaime Carvalho e Silva
Journal: Proc. Amer. Math. Soc. 94 (1985), 612-616
MSC: Primary 35E15
DOI: https://doi.org/10.1090/S0002-9939-1985-0792271-9
MathSciNet review: 792271
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Abstract: We find a necessary and sufficient condition for a Goursat problem for a third order partial differential operator with constant coefficients of the form

$\displaystyle {C_2}({D_x},{D_y}){D_t} + {C_3}({D_x},{D_y})$

to be $ {C^\infty }$-well posed, showing at the same time that a necessary and sufficient condition of Hasegawa cannot be extended. The result can be generalised to operators of higher orders but leads to cumbersome conditions; nevertheless, we show that the condition of Hasegawa is also not sufficient in this case.

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DOI: https://doi.org/10.1090/S0002-9939-1985-0792271-9
Article copyright: © Copyright 1985 American Mathematical Society

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