  We consider the higher-order semilinear parabolic equation $$ \partial_t u =
-(-\Delta)^{m} u + u|u|^{p-1}, $$ in the whole space $\mathbb{R}^N$, where $p >
1$ and $m \geq 1$ is an odd integer. We exhibit type I non self-similar blowup
solutions for this equation and obtain a sharp description of its asymptotic
behavior. The method of construction relies on the spectral analysis of a non
self-adjoint linearized operator in an appropriate scaled variables setting. In
view of known spectral and sectorial properties of the linearized operator
obtained by [Galaktionov, rspa2011], we revisit the technique developed by
[Merle-Zaag, duke1997] for the classical case $m = 1$, which consists in two
steps: the reduction of the problem to a finite dimensional one, then solving
the finite dimensional problem by a classical topological argument based on the
index theory. Our analysis provides a rigorous justification of a formal result
in [Galaktionov, rspa2011].
