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To be more specific, he constructs 4 smooth functions $a(x,t)$, $b(x,t)$, $c(x,t)$, and $u(x,t)$ defined on the strip $\mathbb{R}\times[0,1]$, such that
$$\frac{\partial^8u}{\partial t^8} = a\frac{\partial^4u}{\partial x^4} + b\frac{\partial^2u}{\partial x^2}+cu,$$
$$\frac{\partial^nu}{\partial t^n} = 0,$$
identically on the line $t=0$ for $n=0,\ldots,7$, and $u$ not identically zero.