5 papers
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…
Supercritical Lane-Emden equation on a cone with an inhomogeneous Dirichlet boundary condition
Sho Katayama
We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boun…
Fundamental solution to the heat equation with a dynamical boundary condition
Kazuhiro Ishige, Sho Katayama, Tatsuki Kawakami
We give an explicit representation of the fundamental solution to the heat equation on a half-space of with the homogeneous dynamical boundary condition, and obtain…
Semilinear elliptic problems on the half space with a supercritical nonlinearity
Sho Katayama
This paper concerns positive solutions to the boundary value problems of the scalar field equation in the half space with a Sobolev supercritical nonlinearity and an inhomogeneous…
Supercritical Henon type equation with a forcing term
Kazuhiro Ishige, Sho Katayama
This paper is concerned with the structure of solutions to the elliptic problem for an Henon type equation with a forcing term. Under suitable assumptions on the forcing term, we g…