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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…
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…
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…