Research on spectral structure of dissipative operators and super composition of dissipative systems

耗散算子谱结构及耗散系统超组合研究

• 批准号: 19540189
• 负责人: KADOWAKI Mitsuteru
• 金额: $ 2.83万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540189/
• 关键词: 消散作用素; 波動方程式; スペクトル; 重ね合わせの原理; Parsevalの等式; 半空間自由境界弾性波; レゾルベントの漸近展開; P波とS波; Rayleigh波; 固有作用素(関数)展開定理; 平行平板領域; 消散項付き波動方程式; 散乱解; 敷居値; 平行平板間領域; 消散解; Helmholtz方程式

We mainly did a mathematical research on the wave propagation problem with a weak dissipative (frictional) effect of appearing to physics and engineering. The research was done by using a characteristic frequency of the phenomenon that is called a spectrum. We obtained the following as main results. Concerning acoustic wave propagation in media of weak dissipative effect, we decided the spectral structure and the behavior of waves of the passage of time. Similar results were obtained concerning the reflection phenomenon when electron is entered into atom. We also decided the shape of waves when elastic waves of a half space (for example, seismic waves) is observed at far.

本文主要对物理和工程中出现的具有弱耗散（摩擦）效应的波传播问题进行了数学研究。这项研究是通过使用被称为频谱的现象的特征频率来完成的。我们得到了以下主要结果。关于弱耗散效应介质中的声波传播，我们确定了波随时间推移的谱结构和行为。对电子进入原子时的反射现象也得到了类似的结果。我们还确定了当在远处观察半空间的弹性波（例如地震波）时波的形状。

项目成果

On scattering for wave equ ations with dissipative terms in laye red media (その2)

关于红色介质中具有耗散项的波动方程的散射（第 2 部分）

• 发表时间: 2009
• 作者: K. Saitoh;R. Miyazaki;H. Nakazawa;H. Matsunaga;中澤秀夫;J. Sugie;門脇光輝;N. Yamaoka;渡辺一雄;松井和幸,松永秀章,村上 悟;田中敏;中澤秀夫;山岡直人;中澤秀夫;Satoshi TANAKA;松永秀章,高橋千尋;門脇光輝
• 通讯作者: 門脇光輝

Some results on spect ral analysis of non-selfadjoint operat ors

非自共算子谱分析的一些结果

• 发表时间: 2007
• 作者: Takeshi Harui;Takao Kato;Akira Ohbuchi;M. Motai and H. Usami;H. Nakazawa
• 通讯作者: H. Nakazawa

On decay-nondecay and scattering for schrödinger equations with time dependent complex potentials

具有时间依赖性复势的薛定谔方程的衰变-非衰变和散射

• DOI: 10.2977/prims/1201012385
• 发表时间: 2007
• 作者: K. Mochizuki;T. Motai
• 通讯作者: T. Motai

On wave equations with dissipation II

关于耗散的波动方程 II

• 期刊: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste (掲載決定)
• 作者: Moonja Jeong;Jong-Won Oh;and Masahiko Taniguchi;石崎 克也;H. Nakazawa
• 通讯作者: H. Nakazawa

Decay and scattering for wave equations with dissipations in layered media

层状介质中具有耗散的波动方程的衰减和散射

• 发表时间: 2009
• 作者: K. Saitoh;R. Miyazaki;H. Nakazawa
• 通讯作者: H. Nakazawa