Mathematical analysis of nonlinear partial differential equations describing interaction of several fields

描述多个场相互作用的非线性偏微分方程的数学分析

• 批准号: 21540190
• 负责人: WADA Takeshi
• 金额: $ 2.16万
• 依托单位: Kumamoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540190/
• 关键词: 非線形偏微分方程式; 適切性; 相互作用; 函数方程式論; 非線形Schrodinger方程式; 分散型方程式; 波動方程式

We studied the well-posedness of nonlinear partial differential equations in mathematical physics and their systems. A given problem for a partial differential equation with initial or boundary conditions is called well-posed if the problem has a unique solution, and if the solution depends continuously on the data given in the problem. This is an important step to ensure that the equation correctly describes the phenomenon. In this research we proved the well-posedness of nonlinear Schrodinger equations and the Maxwell-Schrodinger system under appropriate conditions.

研究了数学物理中非线性偏微分方程及其系统的适定性。如果给定问题具有唯一解，且解连续依赖于问题中给出的数据，则具有初始条件或边界条件的偏微分方程的给定问题称为适定的。这是确保方程正确描述现象的重要步骤。本文在适当的条件下证明了非线性薛定谔方程和麦克斯韦-薛定谔方程组的适定性。

项目成果

Scattering theory for the Dirac Equation of Hartree type and the semir elativistic Hartree equation

Hartree型狄拉克方程和半相对论Hartree方程的散射理论

• 发表时间: 2012
• 期刊: Nonlinear Analysis Series A : Theory, Methods and Applications
• 作者: Makoto Nakamura;Kimitoshi Tsutaya
• 通讯作者: Kimitoshi Tsutaya

On well-posedness for nonlinear Schrödinger equations with power nonlinearity in fractional order Sobolev spaces

• DOI: 10.1016/j.jmaa.2012.04.079
• 发表时间: 2012-11
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: H. Uchizono;Takeshi Wada

Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger Equations

• DOI: 10.1016/j.jfa.2012.04.010
• 发表时间: 2012-07
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: Takeshi Wada

空間2次元におけるMaxwell-Schrodinger方程式

二维空间中的麦克斯韦-薛定谔方程

• 发表时间: 2009
• 作者: Alexander Balinsky;W. Desmond Evans;Tomio Umeda;木坂正史;下村哲;T. Suzuki;上木直昌;小野公輔;M. Seto;木坂正史;T.Suzuki;Yoshimi Saito;岩崎千里;T. Shimomura;和田健志;上木直昌;T.Suzuki;宍倉光広;M.Enomoto,Y.Watatani;Chisato Iwasaki;Yoshimi Saito;和田健志
• 通讯作者: 和田健志

SMALL GLOBAL SOLUTIONS FOR NONLINEAR COMPLEX GINZBURG–LANDAU EQUATIONS AND NONLINEAR DISSIPATIVE WAVE EQUATIONS IN SOBOLEV SPACES

非线性复Ginzburg-Landau方程和Sobolev空间中非线性耗散波方程的小全局解

• DOI: 10.1142/s0129055x11004473
• 发表时间: 2011
• 期刊: Reviews in Mathematical Physics
• 影响因子: 1.8
• 作者: Makoto Nakamura