New development of the qualitative theory of nonlinear parabolic and elliptic equations

非线性抛物型和椭圆方程定性理论的新进展

• 批准号: 19204014
• 负责人: YANAGIDA Eiji
• 金额: $ 30.37万
• 依托单位: Tokyo Institute of Technology (2010)Tohoku University (2007-2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19204014/
• 关键词: 関数方程式の大域理論; 非線形; 拡散; 放物型; 楕円型; 偏微分方程式; 定性理論; 反応拡散系; ダイナミクス; 非線形解析

We carried out the investigation about the structure of solutions of nonlinear parabolic and elliptic equations. Our main results are as follows : Next, we studied the existence and uniqueness of solutions with moving singularities for a nonlinear parabolic partial differential equation. We also showed that there exists a solution with a moving singularity that changes its type suddenly., and made clear the asymptotic behavior of singular solutions that converges to a singular steady state. We also studied a chemotaxis system, and made clear the structure of self-similar solutions that blows up by concentrating to a point in finite time.For a reaction-diffusion system, which is called a Gierer-Meinhardt system, we studied the mathematical structure of pattern formation, and also made clear the behavior of time-dependent solutions.

我们对非线性抛物型和椭圆型方程的解的结构进行了研究。我们的主要结果如下：其次，我们研究了一类非线性抛物型偏微分方程具有移动奇点解的存在唯一性。我们还证明了存在一个运动奇点的解，它的类型会突然改变。明确了奇异解收敛到奇异稳态的渐近性态。我们还研究了一个趋化性系统，明确了在有限时间内集中到一点而爆破的自相似解的结构;对于一个反应扩散系统，我们研究了Gierer-Meinhardt系统的模式形成的数学结构，明确了依赖于时间的解的行为.

项目成果

Eigenfunctions of the adjointoperator associated with a pulse solution of some reaction-diffusion systems

与某些反应扩散系统的脉冲解相关的伴随算子的本征函数

• 发表时间: 2008
• 期刊: Bull Inst. Math. Acad. Sin
• 作者: S.-I. Ei;H. Ikeda;K. Ikeda and E. Yanagida
• 通讯作者: K. Ikeda and E. Yanagida

Representation formula for the critical point of the Tadjbakhsh-Odeh functional and its application

Tadjbakhsh-Odeh泛函临界点表示公式及其应用

• 发表时间: 2008
• 期刊: Japan J. Indust. Appl. Math. 25
• 作者: H. Osada;T. Shirai;天形健;I. Takagi
• 通讯作者: I. Takagi

Convergence of anisotropically decaying solutions fora supercritical semilinear heat equation

超临界半线性热方程各向异性衰减解的收敛性

• 发表时间: 2009
• 期刊: J Dyn. Diff. Eqs
• 作者: Kaneko;Masanobu;P. Polacik and E. Yanagida
• 通讯作者: P. Polacik and E. Yanagida

Gradient estimates for the heat equation in the exterior domains under the Neumann boundary condition

诺伊曼边界条件下外域热方程的梯度估计

• 发表时间: 2009
• 期刊: Differential Integral Equations 22
• 作者: J.;Kigami;木上 淳;石毛和弘
• 通讯作者: 石毛和弘

Eigenfunctions of the adjoint operator associated with a pulse solution of some reaction-diffusion systems, Bull.

与某些反应扩散系统的脉冲解相关的伴随算子的本征函数，Bull。

• 发表时间: 2008
• 期刊: Inst. Math. Acad. Sin. (N. S.) 3
• 作者: S.-I. Ei;H. Ikeda;K. Ikeda;E. Yanagida
• 通讯作者: E. Yanagida