Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions

In this paper we discuss the blow-up for classical solutions to the following class of parabolic equations with Robin boundary condition: $\{\begin{array}{cc}{\left(b\left(u\right)\right)}_t=??\left(g\left(u\right)?u\right)+f\left(u\right)\hfill & \text{in }\Omega \times (0,T)\text{,}\hfill \\ \frac{?u}{?n}+\gamma u=0\hfill & \text{on }?\Omega \times (0,T)\text{,}\hfill \\ u(x,0)=h\left(x\right)\ge 0\hfill & \text{in }\overline{\Omega }\text{,}\hfill \end{array}$ where $\Omega$ is a bounded domain of ${\mathbb{R}}^N(N\ge 2)$ with smooth boundary $?\Omega$. By constructing some appropriate auxiliary functions and using a first-order differential inequality technique, we derive conditions on the data which guarantee the blow-up or the global existence of the solution. For the blow-up solution, a lower bound on blow-up time is also obtained. Moreover, some examples are presented to illustrate the applications.