Non-Uniqueness in Hyperbolic Cauchy Problems

Abstract

where t E R and x E Ri', we say that it possesses the uniqueness property at a point (to, xo) if, for any solution u E C'(V) of (1), V being a neighborhood of (t0o xO) such that u 0 on V nf {t < to }, it results that u 0 on a neighborhood of (to, xo). The first uniqueness results for Equation (1) were supplied by the classical theorems of Holmgren [12], Carleman [6] and Calderon [5]; more refined versions of these theorems are the following ones: