Analysis on Fully Nonlinear Elliptic and Parabolic Partial Differential Equations and its Applications

全非线性椭圆抛物型偏微分方程分析及其应用

• 批准号: 22740091
• 负责人: TAKIMOTO Kazuhiro
• 金额: $ 1.91万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740091/
• 关键词: 完全非線形偏微分方程式; 境界値問題; 粘性解; 解の存在と一意性; 関数方程式; 解析学; 完全非線形偏微方程式

We study the solvability of the boundary value problem and the behavior of solutions for fully nonlinear elliptic and parabolic partial differential equations. We also aim for the investigation of nonlinear phenomena. New results are obtained on the uniqueness of solutions to the so-called k-curvature equation, which is a fully nonlinear partial differential equation having geometric structure, and on the dynamics of the parabolic quasilinear problem of mean curvature type.

研究了完全非线性椭圆型和抛物型偏微分方程边值问题的可解性和解的性态。我们也致力于非线性现象的研究。得到了关于所谓的k-曲率方程（这是一个具有几何结构的完全非线性偏微分方程）解的唯一性和关于平均曲率型抛物拟线性问题的动力学的新结果。

项目成果

Bernstein type theorem for Hessian quotient equations, INdAM Workshop (Second Italian-Japanese Workshop)

Hessian 商方程的 Bernstein 型定理，INdAM 研讨会（第二届意大利-日本研讨会）

• 发表时间: 2011
• 作者: Maekawa;Y.;Kazuhiro Takimoto
• 通讯作者: Kazuhiro Takimoto

A quasilinear parabolic perturbation of the linear heat equation

• DOI: 10.1016/j.jde.2011.09.018
• 发表时间: 2012
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: S. Cano-Casanova;J. López-Gómez;Kazuhiro Takimoto

On the existence and uniqueness of boundary blowup solutions to k-curvature equation

k曲率方程边界爆炸解的存在唯一性

• 发表时间: 2010
• 作者: Maekawa;Y.;T. Watanabe;滝本和広;Kazuhiro Takimoto
• 通讯作者: Kazuhiro Takimoto

On the uniqueness of a solution to the boundary blowup problem for curvature equation

曲率方程边界爆炸问题解的唯一性

• 发表时间: 2010
• 作者: Maekawa;Y.;滝本和広;渡部 拓也;滝本和広;Y. Maekawa;Takuya WATANABE;滝本和広;渡部拓也;Y. Maekawa;Kazuhiro Takimoto
• 通讯作者: Kazuhiro Takimoto

A weighted quasilinear equation related to the mean curvature operator

• DOI: 10.1016/j.na.2012.06.004
• 发表时间: 2012-10
• 期刊: Nonlinear Analysis-theory Methods & Applications
• 影响因子: 1.4
• 作者: S. Cano-Casanova;J. López-Gómez;Kazuhiro Takimoto