Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux

A blow-up analysis for a nonlinear divergence form of parabolic equation with time-dependent coefficients is given under nonlinear boundary flux in a bounded star-shaped region. We establish some conditions on time-dependent coefficients and nonlinearities to guarantee existence of global solution or blow-up solution at some finite time t*. Moreover, an upper bound for t* is derived. Under somewhat more restrictive conditions, a lower bound for t* can be obtained. Finally, some application examples to verify the bounds of t* are presented.