论文标题
周期性在三阶边界价值问题解决方案中的作用
The role of periodicity in the solution of third order boundary value problems
论文作者
论文摘要
在这篇简短的论文中，我们阐明了如何在$ [0,1]上$ u_t+u_ {xxx} = 0 $ [0,1] $的某些说明性边界价值问题的解决方案表示为纯粹的周期性问题解决方案的扰动。动机是了解边界条件在解决方案属性中的作用。这在与不连续的初始数据以及复兴和分化现象的线性分散问题解决方案的相关工作中尤为重要。
In this short paper, we elucidate how the solution of certain illustrative boundary value problems for the Airy equation $u_t+u_{xxx}=0$ on $[0,1]$ can be expressed as a perturbation of the solution of the purely periodic problem. The motivation is to understand the role boundary conditions play in the properties of the solution. This is particularly important in related work on the solution of linear dispersive problems with discontinuous initial data and the phenomena of revivals and fractalization.
