Abstract
In this paper we discuss the C1 well-posedness for second order hyperbolic equations Pu D 2 t u a(t , x) 2 x u D f with two independent variables (t , x). Assuming that the C1 function a(t , x) 0 verifies p t a(0, 0) ¤ 0 with some p and that the discriminant 1(x) of a(t , x) vanishes of finite order at x D 0, we prove that the Cauchy problem for P is C1 well-posed in a neighbourhood of the origin.
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