In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with certain boundary disturbances. Based on the weak maximum principle, a classical result on the maximum estimate of solutions to linear parabolic PDEs has been extended, which enables the ISS analysis for certain nonlinear parabolic PDEs with certain boundary disturbances. To illustrate the application of this method, we establish ISS estimates for a linear reaction–diffusion PDE and a generalized Ginzburg–Landau equation with mixed boundary disturbances. Compared to some existing methods, the scheme proposed in this paper involves less intensive computations and can be applied to the ISS analysis for a wide class of nonlinear PDEs with boundary disturbances.

在本文中，我们引入了一种基于弱最大原理的方法，对具有某些边界干扰的某些非线性偏微分方程（PDE）进行输入到状态稳定性（ISS）分析。基于弱最大原理，扩展了线性抛物型PDE解的最大估计的经典结果，这使得对具有某些边界扰动的某些非线性抛物型PDE进行ISS分析。为了说明该方法的应用，我们建立了线性反应扩散PDE和带有混合边界扰动的广义Ginzburg-Landau方程的ISS估计。与现有的一些方法相比，本文提出的方案涉及的计算量较少，并且可以应用于具有边界扰动的多种非线性PDE的ISS分析。