AI 中文总结
本文针对带周期外力的定常粘性Burgers方程，采用直接傅里叶级数方法构造关于粘性一致有界的周期解，所得结果较Jauslin-Kreiss-Moser的工作收敛速度更优。
AI 中文摘要
本文研究带有周期外力的定常粘性Burgers方程的周期问题，主要目标是通过直接傅里叶级数方法构造该模型中关于粘性一致有界的周期解。首先，以带特定外力的无粘性Burgers方程的一个特殊解为起点，显式求解粘性Burgers方程的近似解。其次，通过求解一个二阶常微分方程的初值问题，构造出带外力的粘性Burgers方程周期问题的解，该解关于粘性一致有界。与Jauslin-Kreiss-Moser的结果相比，本文方法为周期解提供了显式构造过程，且当粘性趋于0时，收敛速度更优（可达更高阶）。
英文摘要
In this paper, we consider the periodic problem to steady viscous Burgers equation with an periodic and external force. Our main aim is to construct periodic solutions to this model which are uniformly bounded with respect to the viscosity via a direct Fourier series approach. Firstly, as an example, starting from a special solution of the non-viscous Burgers equation with a specific force, we solve the approximate solutions to the viscous Burgers equation in an explicit way. Secondly, we construct the solution to the periodic problem of the viscous Burgers equation with the external force by solving the initial value problem to a second ordinary differential equations, which is uniformly bounded with respect to the viscosity. Compared with Jauslin-Kreiss-Moser's result, our approach provides an explicit constructive procedure for the periodic solutions and yields a sharper convergence rate (up to higher order) when the viscosity vanishes.
Comments30 pages
