论文标题
使用Sobolev数据的Kirchhoff方程式的全局可溶性
The global solvability of the Kirchhoff equation with Sobolev data
论文作者
论文摘要
我们在Sobolev空间的背景下考虑线性和非线性Cauchy方程。特别是，我们在Sobolev Space中显示了Kirchhoff方程的全球解决方案的全球解决方案，这一问题已经开放了八十年以上。我们的证明是基于针对线性方程的新的均匀估计，该估计是具有时间相关系数和固定点参数。作为我们结果的直接结果，还获得了基尔chhoff方程的全局可溶可在Gevrey空间中具有初始数据的全局可溶性。
We consider linear and non-linear Cauchy equations in the context of Sobolev spaces. In particular, we show the global existence of solutions to the Kirchhoff equation with initial data in the Sobolev spaces, a problem that has been open for more than eighty years. Our proof is based on a new uniform estimate for solutions to the linear equation with time-dependent coefficient and a fixed point argument. As an immediate consequence of our result, the global solvability of the Kirchhoff equation with initial data in the Gevrey spaces is also obtained.
