3 papers
math.AP2024
Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds
Kazuhiro Ishige, Asuka Takatsu, Haruto Tokunaga
We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywher…
math.AP2023
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…
math.AP2014
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…