3 citations · 6 across the 13 of their papers we have counts for
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Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data
Kotaro Hisa, Jin Takahashi, Erbol Zhanpeisov
We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions t…
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…
Non-uniqueness of positive solutions for supercritical semilinear heat equations without scale invariance
Kotaro Hisa, Yasuhito Miyamoto
We establish nonuniqueness of solutions for Cauchy problems of semilinear heat equations with a wide class of nonlinearities. Specifically, we consider \[ \begin{cases} \partial_tu…
Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition
Kotaro Hisa, Kazuhiro Ishige
We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for…
Necessary conditions for the solvability of fractional semilinear heat equations in the very weak framework
Kotaro Hisa
In this paper we obtain necessary conditions on the initial value for the solvability of the Cauchy problem for semilinear heat equations. These necessary conditions were already o…
Threshold property of a singular stationary solution for semilinear heat equations with exponential growth
Kotaro Hisa, Yasuhito Miyamoto
Let . We are concerned with a Cauchy problem of the semilinear heat equation \[ \begin{cases} \partial_tu-Δu=f(u), & x\in\mathbb{R}^N,\ t>0,\\ u(x,0)=u_0(x), & x\in\mathbb{…