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math.AP2025
On blow-up rate for the Hénon parabolic equation with Sobolev supercritical nonlinearity
Kotaro Hisa, Yukihiro Seki
We discuss the Hénon parabolic equation in a finite ball in under the Dirichlet boundary condition, where , , and . W…
math.AP2016
Type II blow-up mechanism for supercritical harmonic map heat flow
Paweł Biernat, Yukihiro Seki
The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flo…
math.AP2012★ 13 cited
Multiple peak aggregations for the Keller-Segel system
Yukihiro Seki, Yoshie Sugiyama, Juan J. L. Velázquez
In this paper we derive matched asymptotic expansions for a solution of the Keller-Segel system in two space dimensions for which the amount of mass aggregation is , where $N=…