6 papers
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…
A general nonlinear characterization of stochastic incompleteness
Gabriele Grillo, Kazuhiro Ishige, Matteo Muratori +1
Stochastic incompleteness of a Riemannian manifold amounts to the nonconservation of probability for the heat semigroup on . We show that this property is equivalent to the…
Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition
Kotaro Hisa, Kazuhiro Ishige
We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for…
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…
A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality
Kazuhiro Ishige, Qing Liu, Paolo Salani
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality…