Scattering and Inverse Scattering for Linear and Nonlinear Wave Propagations

线性和非线性波传播的散射和逆散射

基本信息

批准号：
16540204
负责人：
MOCHIZUKI Kiyoshi
金额：
$ 2.3万
依托单位：
Chuo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540204/
关键词：
Wave equation Schr"odinger equation scattering theory Problem of inverse scattering Inverse scattering on graphs time dependent potential scattering theory time dependent perturbation wave equation Schro" dinger equation inverse scatte

项目摘要

In this project we have been studying several kind of wave propagation phenomena for the fundamental equations of physics like Maxwell equations and Schr"odinger equations. Our main subjects are in the scattering theory and inverse scattering theory, and these problems are important not only in the fields of mathematical analysis but also in those of applied sciences.We shall summarize the results of the head investigator.In [1] is developed the scattering theory for wave equations in exterior domain with coefficients depending on both space and time. The space-time weighted energy estimates play the crucial role in this problem. In [5] we studied similar problems for Schr"odinger equations with time dependent potentials. The space time LAp-LAq estimates becomes important in this problem. In [2] is obtained a Rellich type asymptotic estimates for generalized eigenfunctions for the Schr"odinger operator with oscillating longrange potentials. The results are applied to show the principle of limiting absorption for this operator. [3] is the joint work with Prof. M. Nakao, and a standard decay condition of energy is shown for wave equations in exterior domain with dissipation which is effective only near infinity. In [4] is studied the inverse scattering for Schr"odinger equations on graphs. These problems are recently recognized to be important not only in the classical field of nano-scale technology (like solid state physics and electrionics) but also in the filed of information stechnology. [4] is obtained as a joint work with Profs V. Marchenko and I. Trooshin, and is restricted to the simplest graph including a compact part. Our joint works will proceed into more general graphs including compact parts. Another work is done on the scattering inverse problem for non-selfadjoint wave equation as a continuation of the former work of the same title (Kluwer Academic Publishers, ISAAK 10 (2003), 303-316).

在这个项目中，我们一直在研究诸如麦克斯韦方程和schr“奥德格方程”等物理基本方程的几种波传播现象。我们的主要主题在散射理论和逆散射理论中，这些问题在数学分析领域不仅重要，而且在应用科学的散射中也应逐步散布。系数取决于时空加权估计，在[5]中起着至关重要的作用。在此问题中，时空LAP-LAQ估计变得很重要。 In [2] is obtained a Rellich type asymptotic estimates for generalized eigenfunctions for the Schr"odinger operator with oscillating longrange potentials. The results are applied to show the principle of limiting absorption for this operator. [3] is the joint work with Prof. M. Nakao, and a standard decay condition of energy is shown for wave equations in exterior domain with dissipation which is effective only near infinity. In [4]研究了图上的schr“ odinger方程的反散射。最近，这些问题不仅在纳米级技术的古典领域（例如固态物理学和电子学）中很重要，而且在信息启动学的提交中也很重要。 [4]作为与Marchenko和I. Trooshin教授的联合作品获得的，并仅限于最简单的图表，包括紧凑的部分。我们的联合作品将继续进行更通用的图表，包括紧凑的零件。在非频道浪潮方程的散射反问题上，这是一项工作，这是同一标题以前的作品的延续（Kluwer学术出版商，Isaak 10（2003），303-316）。