Blow-up criteria for reaction diffusion equations with space dependent coefficients

In this paper, we deal with the solutions of global existence and blow-up of solutions under nonlinear boundary conditions with space-dependent coefficients. By constructing auxiliary functions and applying a series of modified differential inequalities, we establish the global existence of classical solutions. Furthermore, we impose suitable conditions on the inner absorption terms to ensure finite time blow-up and derive the estimation of the upper and lower bounds of the blow-up time of solutions when blow-up occurs. Finally, some concrete examples are presented to illustrate the veracity of this paper.