今後のセミナーの予定
Schedules of future seminars
● 2026 年 4 月 27 日 (Mon) 16:00 〜 17:00
- 講演者
- Ulisse Stefanelli 氏 （University of Vienna）
- 講演題目
- A free boundary problem in accretive growth
- 講演要旨
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Accretive growth, in which material is added at the boundary of a system, is a central phenomenon in biology, natural processes, and engineering.
Mathematically, it can be described by a stationary Hamilton-Jacobi equation governing the motion of the boundary, coupled with a PDE for an activation field (such as nutrients, temperature, or stress) defined on the evolving domain.
This results in a free boundary problem with a highly nonlinear, coupled structure.
In this talk, I will present an existence analysis for such a problem.
I will begin with the growth subproblem, where I establish sharp regularity properties of the sublevel sets of the solution.
In particular, I will show that the growing domains satisfy a uniform Poincaré inequality.
This provides the analytical framework needed to prove an existence result for the fully coupled free boundary system.
● 2026 年 5 月 8 日 (Fri) 16:00 〜 17:00
- 講演者
- 藤井 幹大 氏 （名古屋市立大学 大学院理学研究科）
Mikihiro Fujii (Nagoya City University)
- 講演題目
- Sharp non-uniqueness for the Navier–Stokes equations in scaling critical spaces
- 講演要旨
-
3 次元全空間における外力なしの非圧縮性 Navier-Stokes 方程式を考察する．
解の無条件一意性が $C([0,T);L^3)$ において成立することはよく知られた事実であるが，本講演では Triebel-Lizorkin 空間や Besov 空間の意味で $L^3$ を少しでも広い臨界空間に置き替えると，この一意性が破綻することを証明する．
本研究により得られた非一意解は消散性を呈さず，時刻無限大で非自明定常解に収束する．
● 2026 年 5 月 15 日 (Fri) 16:00 〜 17:00
- 講演者
- ザンペイソフ エルボル 氏 （東北大学 大学院理学研究科）
Erbol Zhanpeisov (Tohoku University)
- 講演題目
- Blow-up rate for the subcritical semilinear heat equation in non-convex domains
- 講演要旨
-
We study the blow-up rate for solutions of the subcritical semilinear heat equation.
We prove type I estimates for sign-changing solutions in possibly non-convex domains, extending previous results that required convexity or positivity assumptions.
The proof uses the Giga-Kohn energy together with a geometric inequality controlling the effect of non-convexity.
This is based on joint work with Hideyuki Miura and Jin Takahashi.