実施日：２０２５年７月１２日（土）～７月１３日（日）
開催地：秋田大学手形キャンパス 教育文化学部５号館２階５－２０９
秋田駅からのアクセス：（秋田駅東口）→（駅を背にして直進）→（あっぱれ寿司のある交差点を左折）→（１０分程度直進）→（秋田大学、南門から入ると便利）
Kelei Wang先生には、Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equationの論文解説をしていただきます。
プログラム（pdf）
●７月１２日（土）
１）１３：３０～１４：１０ Kelei Wang（武漢大学） 論文解説１
「Blow up analysis for blow up phenomena in Fujita equation」
２）１４：２０～１５：００ Kelei Wang（武漢大学） 論文解説２
「Blow up analysis for blow up phenomena in Fujita equation」
３）１５：２０～１６：００ Qidi Zhang（香港科技大学）
「Some recent progress in the parabolic gluing method」
４）１６：２０～１７：００ 高棹圭介（京都大学）
「Singular limit of the weighted Allen-Cahn equation」
●７月１３日（日）
１）１０：００～１０：４０ Kelei Wang（武漢大学） 論文解説３
「Blow up analysis for blow up phenomena in Fujita equation」
２）１０：５０～１１：３０ Kelei Wang（武漢大学） 論文解説４
「Blow up analysis for blow up phenomena in Fujita equation」
３）１３：１０～１３：５０ 藤嶋陽平（静岡大学）
「Uniform boundedness of global solutions for non scale invariant superlinear heat equations」
４）１４：１０～１４：５０ Yifu Zhou（武漢大学）
「Singularities in the $H$-system and its heat flow」
５）１５：２０〜１７：２０ 研究討論
アブストラクト
■Kelei Wang（武大・武漢大学）「Blow up analysis for blow up phenomena in Fujita equation」
Since its discovery in 1966 by Fujita, the finite-time blow-up problem for the Fujita equation has attracted the attention of numerous mathematicians. To date, substantial results have been established regarding the classification of blow-ups in the subcritical case and the construction of Type II blow-ups in the critical case. However, the classification in both critical and supercritical cases remains less understood. In this series of talks, I will discuss a blow-up analysis approach to this problem, encompassing:
1. Monotonicity formula and its applications;
2. Tangent flow analysis and its applications (predominantly in the supercritical case);
3. Analysis of bubbling phenomena;
4. Inner-outer decoupling method: dynamics of bubbles in the critical case.
■Qidi Zhang（張啓迪・香港科技大学）「Some recent progress in the parabolic gluing method」
We will present some recent progress on the construction of finite-time singularity, global dynamics especially in the energy-critical heat equation type, harmonic map heat flow, and Landau-Lifshitz-Gilbert equation.
■Keisuke Takasao（高棹圭介・京都大学）「Singular limit of the weighted Allen-Cahn equation 」
We consider a weighted Allen-Cahn equation with a positive potential $K(x)$. Formally, the equation corresponds to a gradient flow of the weighted area functional, that is, the mean curvature flow with transport term $-\nabla^\perp K/(2K)$. In 2018, Qi-Zheng proved that the Allen-Cahn equation converges to the gradient flow in the sense of Brakke when $K \in C^2 (\overline{\Omega})$. We partially extend the results for $K \in W^{2,p} (\Omega)$ where $p>n/2$. In addition, we explain the monotonicity formula and related estimates for the Allen-Cahn equation. This talk is based on a joint work with Hiroki Harashima (TAIJU LIFE INSURANCE COMPANY LIMITED).
■Yohei Fujishima（藤嶋陽平・静岡大学）「Uniform boundedness of global solutions for non scale invariant superlinear heat equations」
We study the uniform boundedness of radially symmetric global solutions for a superlinear heat equation with the Dirichlet boundary condition. For a non scale invariant superlinear heat equation, it is possible to generalize the Sobolev exponent and the Joseph-Lundgren exponent with respect to the growth rate of a nonlinear term, and we show the non existence of grow up solutions under the condition that a generalized growth rate is between the Sobolev exponent and the Joseph-Lundgren exponent. In particular, our results are applicable to a superlinear heat equation with exponential nonlinearity, and it can be seen that grow up solutions do not exist even for the problem with nonlinear terms exhibiting very strong growth in cases of 3 to 9 dimensions. This talk is based on a joint work with Toru Kan (Osaka Metropolitan University).
■Yifu Zhou（周一夫・武漢大学）「Singularities in the $H$-system and its heat flow」
In this talk, we will report some recent construction of bubbling solutions to the $H$-system and its heat flow in two dimensions: finite-time blow-up solution with degree 1 for the heat flow, and multi-bubble solutions with degree 2 for its elliptic counterpart. Key ingredients include the non-degeneracy for the $H$-bubble with any degree, a decoupling property for the linearized system, and the dealing with extra modulation parameters.
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世話人
高橋仁（東京科学大学）、原田潤一（秋田大学）、三浦英之（東京科学大学）、Yifu Zhou（武漢大学）
本ワークショップは、つぎの日本学術振興会_科学研究費の支援を受けて開催されます。
１）基盤研究(B) 23K20803 (代表：三浦英之)「非線形偏微分方程式における解の臨界正則性と特異性」
２）基盤研究(C) 23K03161 (代表：原田潤一)「非線形熱方程式に現れる様々なデルタ関数型特異点の解析」
３）若手研究 23K12998 (代表：髙橋仁)「非線形放物型方程式における特異性の生成と消失の解析」