6 papers
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…
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…
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 $Ï>0…
Well-posedness of Heat Equations with Nonlinearities of Arbitrarily Rapid Growth
Yohei Fujishima, Kotaro Hisa, Robert Laister
We address local- and global-in-time well-posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our r…
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-Îu=f(u), & x\in\mathbb{R}^N,\ t>0,\\ u(x,0)=u_0(x), & x\in\mathbb…
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…