论文标题
带外力的Kirchhoff方程式的路线图
A road map to the blow-up for a Kirchhoff equation with external force
论文作者
论文摘要
众所周知，经典的双曲线kirchhoff方程无限地接受许多简单的模式，即空间变量中只有一个傅立叶成分的时间周期性解决方案。 在本文中，我们假设，对于非线性的合适选择，存在两个具有不同频率的简单模式之间的异斜连接。在这个假设下，我们烹饪了一个强迫的基尔chhoff方程，该方程承认了一种在有限时间内吹出的解决方案，尽管强迫术语的定期性和有限性。 可以使用最大规律性选择强迫项，从而阻止经典全球存在的应用导致分析和准分析类别。
It is well-known that the classical hyperbolic Kirchhoff equation admits infinitely many simple modes, namely time-periodic solutions with only one Fourier component in the space variables. In this paper we assume that, for a suitable choice of the nonlinearity, there exists a heteroclinic connection between two simple modes with different frequencies. Under this assumption, we cook up a forced Kirchhoff equation that admits a solution that blows-up in finite time, despite the regularity and boundedness of the forcing term. The forcing term can be chosen with the maximal regularity that prevents the application of the classical global existence results in analytic and quasi-analytic classes.
