5 papers
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 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 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…
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_1Îu+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\t…