| Abstract: |
| In this talk, we derive an explicit representation of the fundamental solution to the heat equation in a half-space with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds.
We also investigate qualitative properties of the associated solutions, including precise decay estimates.
Furthermore, we analyze the diffusion limits of solutions to the initial--boundary value problem and clarify the role of the diffusive dynamical boundary condition in determining their behavior.
This talk is based on joint work with Prof. K. Ishige (University of Tokyo) and Dr. S. Katayama (Keio University). |
|