In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.

中文翻译：

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关于具有非线性边界条件的抛物线方程的比较定理

本文给出了一类具有非线性边界条件的二阶非线性抛物线系统的新型比较定理，该定理可以涵盖经典的线性边界条件，如齐次狄利克雷边界条件或诺依曼边界条件。我们的比较定理相对于经典定理的优势在于它使我们能够比较满足不同类型边界条件的两个解。作为我们比较定理的应用，我们可以对一些抛物线方程和具有非线性边界条件的系统的爆破解的存在性给出一些新的结果。