Text only print
Full screen print
Today's seminar
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
2025/05/01
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Sho KATAYAMA (The University of Tokyo)
Fundamental solution to the heat equation with a dynamical boundary condition (Japanese)
Sho KATAYAMA (The University of Tokyo)
Fundamental solution to the heat equation with a dynamical boundary condition (Japanese)
[ Abstract ]
We give an explicit representation of the fundamental solution to the heat equation on a half-space of R^N with the homogeneous dynamical boundary condition and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of R^N with the homogeneous dynamical boundary condition. This talk is based on a joint work with Kazuhiro Ishige (Univ. of Tokyo) and Tatsuki Kawakami (Ryukoku Univ.)
We give an explicit representation of the fundamental solution to the heat equation on a half-space of R^N with the homogeneous dynamical boundary condition and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of R^N with the homogeneous dynamical boundary condition. This talk is based on a joint work with Kazuhiro Ishige (Univ. of Tokyo) and Tatsuki Kawakami (Ryukoku Univ.)
