Analysis for nonlinear critical phenomena described by mean field equations

平均场方程描述的非线性临界现象分析

• 批准号: 20340034
• 负责人: SUZUKI Takashi
• 金额: $ 8.57万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340034/
• 关键词: スケーリング; 双対変分構造; 爆発; 凝縮; 量子化; 点渦乱流; 走化性; 熱弾性; 記憶形状物質; 競合的走化性; Lotka-Volterra系; 点渦乱流平均場; Gel’fand 方程式; 退化放物型方程式; Smoluchowski-Poisson方程式; 量子化爆発機構; 解の爆発; 点渦乱流平均場方程式; 漸近的非退化性; 粘弾性記憶形状合金; 圧縮性流体; Hadamard変分; 非線形現象; 変分構造; 自己組織化; 特異性; 非線

Several common mathematical structures are found in the models describing the motion of mean field of many particles, point vortices, and so on. In this project we focused on a series of nonlinear partial differential equations provides with scaling invariance, and also variational structure associated with a variable regarded as field. We rigorously proved several phenomena emerged from the model, such as concentration or homeostasis, and at the same time developed new mathematical tools to approach interactions between species and global dynamics under strong nonlinearities

在描述多粒子平均场、点涡等运动的模型中发现了几种常见的数学结构，本项目重点研究了一系列具有标度不变性的非线性偏微分方程，以及与被视为场的变量相关的变分结构。我们严格证明了模型中出现的一些现象，如浓度或稳态，同时开发了新的数学工具来研究强非线性下物种与全球动力学之间的相互作用

项目成果

On the existence and nonexistence of maximizers associated with Trudinger-Moser type inequalities in unbounded domains

关于无界域中与 Trudinger-Moser 型不等式相关的最大化器的存在与不存在

• 发表时间: 2013
• 期刊: Emerging topics on differential equations and their applications, Nankai series in pure, applied mathematics and theoretical physics
• 作者: Yoshihiro SAWANO;Kozo YABUTA;Michinori Ishiwata
• 通讯作者: Michinori Ishiwata

Stationary Fix-Caginalp equation with non-local term

具有非局部项的平​​稳 Fix-Caginalp 方程

• 发表时间: 2009
• 期刊: Nonlinear Analysis 71
• 作者: T. Suzuki;S. Tasaki
• 通讯作者: S. Tasaki

外部領域におけるStokes半群の重み付きLp-Lq 評価について

关于外域Stokes半群的加权Lp-Lq评估

• 发表时间: 2008
• 作者: Shunsuke Morosawa;Masahiko Taniguchi;Toshihide Futamura;小林孝行
• 通讯作者: 小林孝行

Hardy type inequality and application to the stability of degenerate stationary waves

• DOI: 10.1016/j.jfa.2009.04.003
• 发表时间: 2009-07
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: S. Kawashima;K. Kurata

Semilinear parabolic equation on bounded domain with critical Sobolev exponent

• DOI: 10.1512/iumj.2008.57.3269
• 发表时间: 2008
• 期刊: Indiana University Mathematics Journal
• 影响因子: 1.1
• 作者: Takashi Suzuki