论文标题
真实线上广义的本杰明 - 马动怪方程的准周期库奇问题
The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line
论文作者
论文摘要
本文研究了对实际线路上的准周期初始数据的广义本杰明·巴诺（GBBM）方程的存在和唯一性问题。我们通过使用基督，Damanik-Goldstein和现任作者在多项式衰减的初始傅立叶数据的假设下，通过任意时间范围获得了具有任意时间范围的经典意义的存在和独特性。我们的结果对于指数衰减的初始傅立叶数据有效，因此可以将其视为具有准周期初始数据的GBBM方程的Cauchy-Kovalevskaya定理。
This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data.
