Global existence and blow-up solutions for a class of nonlinear reaction diffusion equations under nonlinear boundary flux

The positive classical solutions of nonlinear reaction diffusion equations is given under nonlinear boundary flux in bounded domain. By constructing auxiliary functions and applying the maximum principle, the sufficient conditions for the existence of global and blow-up solutions are guaranteed. Meanwhile, the estimate of the global solution, the upper bound for "blow-up time", and the upper estimate of "blow-up rate" are specified.