Uniqueness of solutions of partial differential equations when the initial surface is characteristic at a point

Korbly, Letitia J.

doi:10.1090/S0002-9939-1982-0674093-X

Uniqueness of solutions of partial differential equations when the initial surface is characteristic at a point
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by Letitia J. Korbly

Proc. Amer. Math. Soc. 86 (1982), 617-624

DOI: https://doi.org/10.1090/S0002-9939-1982-0674093-X

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Abstract:

Uniqueness in the Cauchy problem for hyperbolic operators degenerate at a point on the initial surface depends on values of the coefficients of the lower order terms. If the operator $P$ is doubly characteristic at the origin with respect to the $t = 0$ line, $P$ has uniqueness for functions which are smooth enough if the coefficient of the ${D_t}$ term does not lie in a certain discrete set of numbers.

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