It is shown that if a function u(x,t) satisfies a backward parabolic inequality in an open set , (x 0,t 0) is a point in Ω and u(x,t 0) vanishes to infinite order at x = x 0, then u(x,t 0) = 0 for all x in the connected component of x 0 in .
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Javier Fernández (2003) studied this question.
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