On the well-posedness of a 𝐶^{∞} Goursat problem for a partial differential operator of order greater than two

Carvalho e Silva, Jaime

doi:10.1090/S0002-9939-1985-0792271-9

On the well-posedness of a $C^ \infty$ Goursat problem for a partial differential operator of order greater than two
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by Jaime Carvalho e Silva PDF

Proc. Amer. Math. Soc. 94 (1985), 612-616 Request permission

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 \[ {C_2}({D_x},{D_y}){D_t} + {C_3}({D_x},{D_y})\] 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.

References

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Linear partial differential operators

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