39 citations · 160 across the 44 of their papers we have counts for
5 papers · 1 filter
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…
Initial traces and solvability of Cauchy problem to a semilinear parabolic system
Yohei Fujishima, Kazuhiro Ishige
Let be a solution to a semilinear parabolic system \[ \mbox{(P)} \qquad \begin{cases} \partial_t u=D_1Δu+v^p\quad & \quad\mbox{in}\quad{\bf R}^N\times(0,T),\\ \partial_t v=…
Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary condi…
Parabolic Minkowski convolutions of viscosity solutions to fully nonlinear equations
Kazuhiro Ishige, Qing Liu, Paolo Salani
This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of in…
A supercritical scalar field equation with a forcing term
Kazuhiro Ishige, Shinya Okabe, Tokushi Sato
This paper is concerned with the elliptic problem for a scalar field equation with a forcing term \begin{equation} \tag{P}-Δu+u=u^p+ κμ\quad \mbox{in} \quad{\bf R}^N, \quad u>0 \qu…