4 citations · 6 across the 11 of their papers we have counts for
12 papers
Existence of a separating norm for the semilinear heat equation
Jin Takahashi
We consider the initial value problem of the semilinear heat equation in the Fujita supercritical range for which global-in-time solutions may exist. The main result shows the exis…
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…
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 a semilinear heat equation on Riemannian manifolds
Jin Takahashi, Hikaru Yamamoto
We study the solvability of the initial value problem for the semilinear heat equation in a Riemannian manifold with a nonnegative Radon measure on as init…
Blow-up of the critical norm for a supercritical semilinear heat equation
Hideyuki Miura, Jin Takahashi
We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation in an arbitrary smooth domain of . In the rang…
Infinite-time incompleteness of noncompact Yamabe flow
Jin Takahashi, Hikaru Yamamoto
We show the noninheritance of the completeness of the noncompact Yamabe flow. Our main theorem states the existence of a long time solution which is complete for each time and conv…
Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation
Marek Fila, Petra Macková, Jin Takahashi +1
The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solution…
Solutions with snaking singularities for the fast diffusion equation
M. Fila, J. R. King, J. Takahashi +1
We construct solutions of the fast diffusion equation, which exist for all and are singular on the set , , where $ξ\in…
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 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…
Solutions with time-dependent singular sets for the heat equation with absorption
Jin Takahashi, Hikaru Yamamoto
We consider the heat equation with a superlinear absorption term in and study the existence and nonexistence of nonnegative solutions wit…
Removability of time-dependent singularities in the heat equation
Jin Takahashi, Eiji Yanagida
We consider solutions of the linear heat equation with time-dependent singularities. It is shown that if a singularity is weaker than the order of the fundamental solution of the L…