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

首席调查员应邀在一次会议上发言；线性和非线性双曲方程（9月18-21,200，意大利格拉多），并在本次会议上阅读了题为“非线性各向同性弹性波的数学理论”的论文。2003年，我还就上述论文的内容和未解决的数学问题，撰写了一份题为《弹性数学理论》的报告。该报告对今后研究非线性各向同性弹性波有一定的参考价值。这篇题为《各向同性弹性波动方程解的加权均匀衰减估计》的论文发表在《adva . math . sci . application》杂志上。， vol.12(1), 2002。本文保证了《非线性弹性波的全局存在性》这篇发表在《发明数学》杂志上的论文的结果。， vol.142(1), 2000。2003年3月，研究者K.Tsutaya与布朗大学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《具有势和三次卷积的波动方程的整体存在和爆破》发表在《非线性分析》杂志上，是他们讨论的结果之一。

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.