Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Hisa, Kotaro"'
Autor:
Bui, The Anh, Hisa, Kotaro
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 the Heisenberg group $\mathbb{H}^N$. Using these conditions, we can pr
Externí odkaz:
http://arxiv.org/abs/2408.16985
Autor:
Hisa, Kotaro
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 unbounded and disconnected) with a smooth boundary. Our conditions enable
Externí odkaz:
http://arxiv.org/abs/2312.10969
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical
Externí odkaz:
http://arxiv.org/abs/2308.05240
Autor:
Hisa, Kotaro, Kojima, Mizuki
We are concerned with the following time-fractional semilinear heat equation in the $N$-dimensional whole space ${\bf R}^N$ with $N \geq 1$. \[ {\rm (P)}_\alpha \qquad \partial_t^\alpha u -\Delta u = u^p,\quad t>0,\,\,\, x\in{\bf R}^N, \qquad u(0) =
Externí odkaz:
http://arxiv.org/abs/2307.16491
We show the existence and the uniqueness of initial traces of nonnegative solutions to a semilinear heat equation on a half space of ${\mathbb R}^N$ under the zero Dirichlet boundary condition. Furthermore, we obtain necessary conditions and sufficie
Externí odkaz:
http://arxiv.org/abs/2209.06398
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 conditions are sharp and clarify the relationship between the solvability o
Externí odkaz:
http://arxiv.org/abs/2204.08243
Publikováno v:
In Journal de mathématiques pures et appliquées June 2024 186:150-175
Autor:
Hisa, Kotaro, Takahashi, Jin
We consider the Cauchy problem for the Hardy parabolic equation $\partial_t u-\Delta u=|x|^{-\gamma}u^p$ with initial data $u_0$ singular at some point $z$. Our main results show that, if $z\neq 0$, then the optimal strength of the singularity of $u_
Externí odkaz:
http://arxiv.org/abs/2102.04618
Autor:
Hisa, Kotaro, Sierżęga, Mikołaj
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 +(-\Delta)^\frac{\theta}{2} u=|x|^{-\gamma} u^p ,\quad x\in{\bf R}^N, t>0, \qquad u(0)
Externí odkaz:
http://arxiv.org/abs/2102.04079
Autor:
Hisa, Kotaro
Consider the heat equation with a nonlinear boundary condition $$ \partial_t u=\Delta u,\quad x\in{\bf R}^N_+,\,\,\,t>0,\qquad \partial_\nu u=u^p, \quad x\in\partial{\bf R}^N_+,\,\,\,t>0,\qquad u(x,0)=\kappa\psi(x),\quad x\in D:=\overline{{\bf R}^N_+
Externí odkaz:
http://arxiv.org/abs/2002.10806