Kirchhoff方程在整体解附近的几乎整体存在性
Almost global existence for Kirchhoff equations around global solutions
摘要：
众所周知，当初始数据趋于零时，Kirchhoff方程解的寿命趋于无穷大。这些结果通常被称为几乎全局存在性，至少在零解的邻域内。在这里，我们扩展这个结果表明，解决方案的寿命是较低的连续性，特别是它往往是无限的，每当初始数据往往是一些有限的数据，起源一个全球性的解决方案。我们还提供了一个估计，从下面的寿命的解决方案时，初始数据接近的一些类的数据，其中全球存在是已知的，即数据与许多傅立叶模式，分析数据和准分析数据。
英文摘要：
It is well-known that the life span of solutions to Kirchhoff equations tends to infinity when initial data tend to zero. These results are usually referred to as almost global existence, at least in a neighborhood of the null solution. Here we extend this result by showing that the life span of solutions is lower semicontinuous, and in particular it tends to infinity whenever initial data tend to some limiting datum that originates a global solution. We also provide an estimate from below for the life span of solutions when initial data are close to some of the classes of data for which global existence is known, namely data with finitely many Fourier modes, analytic data and quasi-analytic data.
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