Abstract
In this paper, we study the higher-order semilinear parabolic equation {u t +(-Δ) m u=a|u| p-1 u, (t,x) ∈ℝ 1 + × ℝ N , u(0,x)=ϕ(x), x∈ℝ N , where m, p>1 and a ∈ ℝ. For p>1 +2m/N, we prove that the global existence of mild solutions for small initial data with respect to some norm. Some of those solutions are proved to be asymptotic self-similar.
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