论文标题
用空间积分项作为部分积分方程的线性PDE的表示
Representation of linear PDEs with spatial integral terms as Partial Integral Equations
论文作者
论文摘要
在本文中，我们介绍了一个空间维度的线性部分微分方程（PDE）的部分积分方程（PIE）表示，其中PDE具有在动力学和边界条件中出现的空间积分项。通过进行变量更改，在每个PDE状态都被微积分的基本定理以获得新方程（pie）的基本定理以取代其最高，明确的衍生物，从而获得了PIE表示。我们表明，从PDE表示到PIE表示的这种转换可以用从PDE参数到PIE参数的明确图来编写。最后，我们提出数值示例，以通过凸优化方法对PDE进行稳定性分析来证明PIE表示的应用。
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary conditions. The PIE representation is obtained by performing a change of variable where every PDE state is replaced by its highest, well-defined derivative using the Fundamental Theorem of Calculus to obtain a new equation (a PIE). We show that this conversion from PDE representation to PIE representation can be written in terms of explicit maps from the PDE parameters to PIE parameters. Lastly, we present numerical examples to demonstrate the application of the PIE representation by performing stability analysis of PDEs via convex optimization methods.
