We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the literature and thus allows the nonlinearities to have arbitrary polynomial growth. We show that two dimensional reaction-diffusion systems, with quadratic intermediate sum conditions, have global solutions which are bounded uniformly in time. In higher dimension, bounded solutions are obtained under the condition that the diffusion coefficients are {\it quasi-uniform}, i.e. they are close to each other. Applications include boundedness of solutions to chemical reaction networks with diffusion.

中文翻译：

---

具有李雅普诺夫函数和中间和条件的反应扩散系统的有界性

我们研究了具有类李雅普诺夫函数并满足 {\it 中间和条件}的反应扩散系统解的均匀有界性。这极大地概括了文献中的质量耗散条件，因此允许非线性具有任意多项式增长。我们展示了二维反应扩散系统，具有二次中间和条件，具有在时间上均匀有界的全局解。在更高维度上，在扩散系数为{\it quasi-uniform}，即它们彼此接近的条件下获得有界解。应用包括具有扩散的化学反应网络的解的有界性。