4 papers · 1 filter
Fundamental solution and diffusion limits for the heat equation in a half-space with a diffusive dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of with a diffusive dynamical boundary condition, and establis…
A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition
Kensho Araya, Kazuhiro Ishige
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: g…
Initial traces and solvability of the fast diffusion equation with power-type nonlinearity
Kazuhiro Ishige, Nobuhito Miyake
We investigate the qualitative behavior of the initial traces of nonnegative solutions to the fast diffusion equation with power-type nonlinearity. Necessary conditions for the exi…
Initial traces and solvability of porous medium equation with power nonlinearity
Kazuhiro Ishige, Nobuhito Miyake, Ryuichi Sato
In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existenc…