Asymptotic analysis and inverse problems for linear and non-linear Helmholtz type equations

线性和非线性亥姆霍兹型方程的渐近分析和反问题

• 批准号: 23740104
• 负责人: WATANABE Michiyuki
• 金额: $ 1.75万
• 依托单位: Niigata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740104/
• 关键词: 関数方程式; 偏微分方程式論; 散乱理論; 逆問題; 解析学; 関数方程式論; 数理物理; 散乱問題

An elastic wave equation in a homogeneous, isotropic, elastic half-space with a free boundary and with a constant density and constant body-wave velocities has been investigated as a simple model of the equation describing the seismic wave propagation. We study a relation between asymptotic behavior of a generalized eigenfunction to the stationary elastic wave equation and the Fourier transform associated with the elastic wave equation. In this research, we obtained that the set of solutions can be described by the Fourier transform and the asymptotic expansion of the solution can be evaluated for all direction.

作为描述地震波传播方程的简单模型，研究了均匀、各向同性、弹性半空间中具有自由边界、具有恒定密度和恒定体波速度的弹性波动方程。研究了定常弹性波动方程广义本征函数的渐近性与弹性波动方程的傅立叶变换之间的关系。在这项研究中，我们得到了解的集合可以用傅立叶变换来描述，并且解的渐近展开式可以在各个方向上估计。

项目成果

Inverse scattering at fixed amplitude for nonlinear Schroedinger equations

非线性薛定谔方程的固定振幅逆散射

• 发表时间: 2012
• 作者: O.Hatori;Y.Iida;S.Stevic;S.Ueki;野津裕史;梅原守道;H. Notsu;A.K. Sharma and S. Ueki;羽鳥理;Ege Fujikawa;Ege Fujikawa;Ege Fujikawa;Michiyuki Watanabe;野津裕史，田端正久;渡邊 道之
• 通讯作者: 渡邊 道之

Inverse Scattering for the Stationary Wave equation with a Friction Term in Two Dimensions

具有二维摩擦项的稳态波动方程的逆散射

• DOI: 10.4171/prims/100
• 发表时间: 2013
• 期刊: Publications of Research Institute for Mathematical Sciences
• 作者: O.Hatori;Y.Iida;S.Stevic;S.Ueki;野津裕史;梅原守道;H. Notsu;A.K. Sharma and S. Ueki;羽鳥理;Ege Fujikawa;Ege Fujikawa;Ege Fujikawa;Michiyuki Watanabe
• 通讯作者: Michiyuki Watanabe