论文标题
小型全球无效汉堡方程的可控性
Small-time global null controllability of generalized Burgers' equations
论文作者
论文摘要
在本文中，我们研究了广义汉堡方程的小全球无效可控性$ y_t +γ| y |^{γ-1} y_x-y__ {xx} = u（t）$ [0,1] $。标量控制$ u（t）$在空间上是统一的，并且在更高维度的压力上起着类似的作用。我们设置了一个右Dirichlet边界条件$ y（t，1）= 0 $，并允许左边界控制$ y（t，0）= v（t）$。在假设$γ> 3/2 $下，我们证明该系统是可以进行的小型全局零控制。我们的证明依赖于返回方法以及对边界层的形状和耗散的仔细分析。
In this paper, we study the small-time global null controllability of the generalized Burgers' equations $y_t + γ|y|^{γ-1}y_x-y_{xx}=u(t)$ on the segment $[0,1]$. The scalar control $u(t)$ is uniform in space and plays a role similar to the pressure in higher dimension. We set a right Dirichlet boundary condition $y(t,1)=0$, and allow a left boundary control $y(t,0)=v(t)$. Under the assumption $γ>3/2$ we prove that the system is small-time global null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer.
