5 papers · 1 filter
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…
Riemannian starshape and capacitary problems
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restr…
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…
Eventual concavity properties of the heat flow
Kazuhiro Ishige
The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of…
Heat equation with a nonlinear boundary condition and uniformly local spaces
Kazuhiro Ishige, Ryuichi Sato
We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local spaces. Furt…