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

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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.