Abstract This paper presents a maximum principle-based approach in the establishment of ISS-like estimates for a class of nonlinear parabolic partial differential equations (PDEs) with variable coefficients and different types of nonlinear boundary conditions on higher dimensional domains. Comparing with the existing literature, the ISS-like estimates established in this paper are independent of the nonlinear terms of the PDEs. Technical development on ISS analysis of the considered systems is detailed, and an example of establishing ISS-like estimates for a nonlinear parabolic equation with, respectively, a nonlinear Robin boundary condition and a nonlinear Dirichlet boundary condition is provided to illustrate the application of the developed method.

中文翻译：

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在高维域上具有可变系数的非线性抛物线偏微分方程的类 ISS 估计

摘要 本文提出了一种基于最大原理的方法，用于在高维域上为一类具有可变系数和不同类型非线性边界条件的非线性抛物线偏微分方程 (PDE) 建立类 ISS 估计。与现有文献相比，本文建立的类 ISS 估计独立于偏微分方程的非线性项。详细介绍了对所考虑系统的 ISS 分析的技术开发，并提供了分别使用非线性 Robin 边界条件和非线性 Dirichlet 边界条件为非线性抛物线方程建立类 ISS 估计的示例，以说明所开发的应用方法。