39 citations · 160 across the 44 of their papers we have counts for
5 papers · 2 filters
Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami +1
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of…
Large time behavior of ODE type solutions to nonlinear diffusion equations
Junyong Eom, Kazuhiro Ishige
Consider the Cauchy problem for a nonlinear diffusion equation \begin{equation} \tag{P} \left\{ \begin{array}{ll} \partial_t u=Δu^m+u^α& \quad\mbox{in}\quad{\bf R}^N\times(0,\infty…
To logconcavity and beyond
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
In 1976 Brascamp and Lieb proved that the heat flow preserves logconcavity. In this paper, introducing a variation of concavity, we show that it preserves in fact a stronger proper…
Nonlinear characterizations of stochastic completeness
Gabriele Grillo, Kazuhiro Ishige, Matteo Muratori
We prove that conservation of probability for the free heat semigroup on a Riemannian manifold (namely stochastic completeness), hence a linear property, is equivalent to uniqu…
Hot spots of solutions to the heat equation with inverse square potential
Kazuhiro Ishige, Yoshitsugu Kabeya, Asato Mukai
We investigate the large time behavior of the hot spots of the solution to the Cauchy problem for the heat equation with a potential , where dec…