Global existence and blow-up for solutions to nonlinear elastic waves

非线性弹性波解的全局存在和爆炸

• 批准号: 13640202
• 负责人: AGEMI Rentaro
• 金额: $ 2.18万
• 依托单位: Future University-HAKODATE
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640202/
• 关键词: Hyperbolic systems; Global existence and blow up; Nonlinear elastic waves; Isotropic materials; Weighted uniform decay estimates; Null Condition; 双曲型方程式; 弾性ポテンシャル; 外部境界値問題; null condition

The head investigator was invited as a speaker of a conference ; Linear and Nonlinear Hyperbolic Equations (Sep.18-21,200, Grado Italy) and read a paper titled by Mathematical theory of nonlinear isotropic elastic waves in this conference. I also made out in 2003 a report, titled by Mathematical theory of elasticity, on the contents of the above paper and the unsolved mathematical problems. This report is very useful for peoples studying nonlinear isotropic elastic waves in future. The paper titled by Weighted uniform decay estimates for solutions to isotropic elastic wave equations was published in the journal, Adv.Math.Sci.Appl., vol.12 (1), 2002. This paper guarantees results of the paper, Global existence of nonlinear elastic waves, published in the journal, Invent.Math., vol.142(1), 2000. An investigator, K.Tsutaya, discussed an initial value problem for a nonlinear wave equation having a cubic convolution with Professor W.Strauss at Brown university in Mar.2003. His paper titled by Global existence and blow up of a wave equation with a potential and a cubic convolution, in press in the journal Nonlinear Analysis is one of results of their discussions.

研究负责人应邀在2000年9月18 - 21日格拉多意大利举行的“线性和非线性双曲方程”会议上发言，并宣读了题为“非线性各向同性弹性波的数学理论”的论文。2003年，我就上述论文的内容和未解决的数学问题作了题为《弹性力学的数学理论》的报告。这对人们今后研究非线性各向同性弹性波具有重要意义。这篇题为《各向同性弹性波方程解的加权均匀衰减估计》的论文发表在《Adv.Math.Sci.Appl.》杂志上，vol.12（1），2002.本文保证了论文的结果，非线性弹性波的整体存在，发表在杂志上，发明数学，第142（1）卷，2000年。2003年3月，Tsutaya先生在布朗大学与W.Strauss教授讨论了具有三次卷积的非线性波动方程的初值问题。他的论文标题为全球存在和爆破的波动方程的潜力和立方卷积，在新闻杂志上的非线性分析是他们的讨论结果之一。

项目成果

津田谷 公利: "Global existence and blow up for a wave equation with a potential and a cubic convolution"Nonlinear Analysis. (In press).

Kimitoshi Tsudaya：“具有势和三次卷积的波动方程的全局存在和爆炸”非线性分析（正在出版）。

Rentaro Agemi: "Weighted uniform decay estimates for solutions to isotropic elastic wave equations"Adv.Math.Sci.Appl.. 12(1). 151-173 (2002)

Rentaro Agemi：“各向同性弹性波方程解的加权均匀衰减估计”Adv.Math.Sci.Appl.. 12(1)。

上見 練太郎: "Weighted uniform decay estimates for solutions to isotropic elasticity equations"Adv. Math. Sci. Appl.. 12(1). 151-173 (2002)

Rentaro Kamimi：“各向同性弹性方程解的加权均匀衰减估计”Adv。12（1）（2002）。

上見 練太郎: "Weighted uniform decay estimates for solutions to isotropic elastic Wave equations"Adv.Math.Sci.Appl.. 12(1). 151-173 (2002)

Rentaro Kamimi：“各向同性弹性波方程解的加权均匀衰减估计”Adv.Math.Sci.Appl.. 12(1) (2002)。