论文标题
部分可观测时空混沌系统的无模型预测
Synchronisation for scalar conservation laws via Dirichlet boundary
论文作者
论文摘要
我们为具有差异元素边界条件的域上的标量保护定律提供了基本的几何同步证明。与以前的结果不同，我们的证明不依赖严格的最大原则，而是基于边界耗散的定量估计。我们确定了一种强制性条件，在所有初始条件下，通过构建合适的超级和子溶液，估计值在所有初始条件下都是均匀的。由于缺乏这种顽强性，我们的结果基于LP能量估计和Lyapunov结构。
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a quantitative estimate of the dissipation at the boundary. We identify a coercivity condition under which the estimates are uniform over all initial conditions, via the construction of suitable super- and sub-solutions. In lack of such coercivity our results build on Lp energy estimates and a Lyapunov structure.
