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Tuesday Seminar of Analysis
Seminar information archive ～12/24｜Next seminar｜Future seminars 12/25～
| Date, time & place | Tuesday 16:00 - 17:30 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, MIYAMOTO Yasuhito, SAKAI Hidetaka, MITAKE Hiroyoshi, TAKADA Ryo |
Future seminars
2026/01/13
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Erbol Zhanpeisov (Tohoku University)
Blow-up rate for the subcritical semilinear heat equation in non-convex domains (Japanese)
Erbol Zhanpeisov (Tohoku University)
Blow-up rate for the subcritical semilinear heat equation in non-convex domains (Japanese)
[ Abstract ]
We study the blow-up rate for solutions of the subcritical semilinear heat equation. Type I blow-up means that the rate agrees with that of the associated ODE. In the Sobolev subcritical range, type I estimates have been proved for positive solutions in convex or general domains (Giga–Kohn ’87; Quittner ’21) and for sign-changing solutions in convex domains (Giga–Matsui–Sasayama ’04). We extend these results to sign-changing solutions in possibly non-convex domains. The proof uses the Giga-Kohn energy together with a geometric inequality that controls the effect of non-convexity. As a corollary, we obtain blow-up of the scaling critical norm in the subcritical range. Based on joint work with Hideyuki Miura and Jin Takahashi (Institute of Science Tokyo).
We study the blow-up rate for solutions of the subcritical semilinear heat equation. Type I blow-up means that the rate agrees with that of the associated ODE. In the Sobolev subcritical range, type I estimates have been proved for positive solutions in convex or general domains (Giga–Kohn ’87; Quittner ’21) and for sign-changing solutions in convex domains (Giga–Matsui–Sasayama ’04). We extend these results to sign-changing solutions in possibly non-convex domains. The proof uses the Giga-Kohn energy together with a geometric inequality that controls the effect of non-convexity. As a corollary, we obtain blow-up of the scaling critical norm in the subcritical range. Based on joint work with Hideyuki Miura and Jin Takahashi (Institute of Science Tokyo).
