3 citations · 9 across the 19 of their papers we have counts for
19 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…
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…
Atmospheric Predictability Beyond 30 Days with Machine Learning
P. Trent Vonich, Gregory J. Hakim
Atmospheric predictability research has long held that rapid error growth at small spatial scales imposes an intrinsic limit of roughly two weeks on deterministic weather forecast…
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{…
Existence of solutions semilinear parabolic equations with singular initial data in the Heisenberg group
The Anh Bui, Kotaro Hisa
In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of fractional semilinear heat equations with power nonlinearities in…
Optimal singularities of initial data of a fractional semilinear heat equation in open sets
Kotaro Hisa
We consider necessary conditions and sufficient conditions on the solvability of the Cauchy--Dirichlet problem for a fractional semilinear heat equation in open sets (possibly unbo…
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for loca…
On solvability of a time-fractional semilinear heat equation, and its quantitative approach to the classical counterpart
Kotaro Hisa, Mizuki Kojima
We are concerned with the following time-fractional semilinear heat equation in the -dimensional whole space with . \[ {\rm (P)}_α\qquad \partial_t^αu -Δu…
Initial traces and solvability for a semilinear heat equation on a half space of
Kotaro Hisa, Kazuhiro Ishige, Jin Takahashi
We show the existence and the uniqueness of initial traces of nonnegative solutions to a semilinear heat equation on a half space of under the zero Dirichlet bounda…
Solvability of Superlinear Fractional Parabolic Equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our condi…
Optimal singularities of initial data for solvability of the Hardy parabolic equation
Kotaro Hisa, Jin Takahashi
We consider the Cauchy problem for the Hardy parabolic equation with initial data singular at some point . Our main results show that, if $z\…
Existence and nonexistence of solutions to the Hardy parabolic equation
Kotaro Hisa, Mikołaj Sierżęga
In this paper, we obtain necessary conditions and sufficient conditions on the initial data for the local-in-time solvability of the Cauchy problem \[ \partial_t u +(-Δ)^\fracθ{2}…
Sharp estimate of the life span of solutions to the heat equation with a nonlinear boundary condition
Kotaro Hisa
Consider the heat equation with a nonlinear boundary condition $$ \partial_t u=Δu,\quad x\in{\bf R}^N_+,\,\,\,t>0,\qquad \partial_νu=u^p, \quad x\in\partial{\bf R}^N_+,\,\,\,t>0,\q…
Existence of solutions for an inhomogeneous fractional semilinear heat equation
Kotaro Hisa, Kazuhiro Ishige, Jin Takahashi
We obtain necessary conditions and sufficient conditions on the existence of solutions to the Cauchy problem for a fractional semilinear heat equation with an inhomogeneous term. W…
Solvability of the heat equation with a nonlinear boundary condition
Kotaro Hisa, Kazuhiro Ishige
We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of with a nonlinear boundary condition. Furthermore, w…
Existence of solutions for a fractional semilinear parabolic equation with singular initial data
Kotaro Hisa, Kazuhiro Ishige
In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem $$ \partial_t u+(-Δ)^{\fracθ{2}}u=u^p,\quad x\i…