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Fundamental solution and diffusion limits for the heat equation in a half-space with a diffusive dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of with a diffusive dynamical boundary condition, and establis…
Existence and uniqueness of -solutions to time-fractional nonlinear diffusion equations
Mikiya Kametaka, Tatsuki Kawakami
We establish the global existence and uniqueness of -solutions to the Cauchy problem for time-fractional porous medium type nonlinear diffusion equations. Furthermore, we give…
Fundamental solution to the heat equation with a dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We give an explicit representation of the fundamental solution to the heat equation on a half-space of with the homogeneous dynamical boundary condition, and obtain…
Existence of solutions for a semilinear parabolic system with singular initial data
Yohei Fujishima, Kazuhiro Ishige, Tatsuki Kawakami
Let be a solution to the Cauchy problem for a semilinear parabolic system \[ \mathrm{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\ti…
Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term
Kazuhiro Ishige, Tatsuki Kawakami, Ryo Takada
We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat…
Existence of solutions to a fractional semilinear heat equation in uniformly local weak Zygmund type spaces
Norisuke Ioku, Kazuhiro Ishige, Tatsuki Kawakami
In this paper we introduce uniformly local weak Zygmund type spaces, and obtain an optimal sufficient condition for the existence of solutions to the critical fractional semilinear…