In the paper, we investigate global and blow-up solutions for a class of nonlinear reaction diffusion equations with Robin boundary conditions. By using auxiliary functions and a first-order differential inequality technique, we establish conditions on the data to prove the existence of global solution. Moreover, based on maximum principles, we obtain a criterion that guarantees the occurrence of the blow-up. When blow-up occurs, we discuss an upper bound and a lower bound on blow-up time. At last, we apply two examples to illustrate our main results.

中文翻译：

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具有Robin边界条件的非线性反应扩散方程的整体解和爆破解

在本文中，我们研究了具有Robin边界条件的一类非线性反应扩散方程的整体解和爆破解。通过使用辅助函数和一阶微分不等式技术，我们在数据上建立条件以证明全局解的存在。此外，基于最大原则，我们获得了保证发生爆炸的标准。当发生爆炸时，我们讨论爆炸时间的上限和下限。最后，我们用两个例子来说明我们的主要结果。