39 citations · 160 across the 44 of their papers we have counts for
45 papers
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_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…
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…
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…
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for loca…
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…
Supercritical Henon type equation with a forcing term
Kazuhiro Ishige, Sho Katayama
This paper is concerned with the structure of solutions to the elliptic problem for an Henon type equation with a forcing term. Under suitable assumptions on the forcing term, we g…
Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions s…
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…
Characterization of -concavity preserved by the Dirichlet heat flow
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
-concavity is a generalization of power concavity and, actually, the largest available generalization of the notion of concavity. We characterize the -concavities preserved b…
Solvability of Superlinear Fractional Parabolic Equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our condi…
Refined asymptotic expansions of solutions to fractional diffusion equations
Kazuhiro Ishige, Tatsuki Kawakami
In this paper, as an improvement of the paper [K. Ishige, T. Kawakami and H. Michihisa, SIAM J. Math. Anal. 49 (2017) pp. 2167--2190], we obtain the higher order asymptotic expansi…
General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data
Goro Akagi, Kazuhiro Ishige, Ryuichi Sato
This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable…
Power concavity and Dirichlet heat flow
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We show that log-concavity is the weakest power concavity preserved by the Dirichlet heat flow in -dimensional convex domains, where (indeed, we prove that starting wit…
Existence of solutions to nonlinear parabolic equations via majorant integral kernel
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order s…
Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II
Kazuhiro Ishige, Yujiro Tateishi
Let be a nonnegative Schrödinger operator on , where and is a radially symmetric inverse square potential. Let $\|\nabla^αe^{-tH}\|_{(L^{p,σ}…
Optimal singularities of initial functions for solvability of a semilinear parabolic system
Yohei Fujishima, Kazuhiro Ishige
Let be a nonnegative solution to the semilinear parabolic system \[ \mbox{(P)} \qquad \cases{ \partial_t u=D_1Δu+v^p, & \\ \partial_t v=D_2Δv+u^q,…
Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces
Kazuhiro Ishige, Yujiro Tateishi
Let be a nonnegative Schrödinger operator on , where and is an inverse square potential. In this paper we obtain sharp decay estimates of the…
New characterizations of log-concavity
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We introduce a notion of -concavity which largely generalizes the usual concavity. By the use of the notions of closedness under positive scalar multiplication and closedness un…
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence t…
Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applica…
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…